Necessary and Sufficient Conditions for Circulant Digraphs to be Antistrong, Weakly-Antistrong and Anti-Eulerian
Abstract An antidirected trail in a digraph is a trail (a walk with no arc repeated) in which the consecutive arcs have opposite directions. The forward antidirected trails are special antidirected trails which begin and end with forward arcs. A digraph D containing a forward antidirected (x, y)-tra...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Yuan, Lili [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2023 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Übergeordnetes Werk: |
Enthalten in: Graphs and combinatorics - Tokyo : Springer-Verl. Tokyo, 1985, 39(2023), 2 vom: 16. Feb. |
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| Übergeordnetes Werk: |
volume:39 ; year:2023 ; number:2 ; day:16 ; month:02 |
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| DOI / URN: |
10.1007/s00373-023-02620-4 |
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| Katalog-ID: |
SPR049348876 |
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| 520 | |a Abstract An antidirected trail in a digraph is a trail (a walk with no arc repeated) in which the consecutive arcs have opposite directions. The forward antidirected trails are special antidirected trails which begin and end with forward arcs. A digraph D containing a forward antidirected (x, y)-trail for every choice of %$x,y\in V(D)%$ is called antistrong. An antidirected trail which begins with a forward arc and ends with a backward arc is a forward-backward antidirected trail. For any %$x,y\in V(D)%$, if digraph D has a forward antidirected (x, y)-trail or a forward-backward antidirected (x, y)-trail, then D is weakly-antistrong. A digraph is anti-Eulerian if it admits a closed anti-directed Euler trail. Let %$BC(Z_n, C)%$ be a Bi-Circulant graph with %$n\ge 3%$ and %$C=\{j_1, j_2, \ldots , j_{l}\}%$, %$l\ge 2%$. This paper shows that the number of connected components of %$BC(Z_n, C)%$ is equal to %$gcd(j_1-j_l, \ldots , j_{l-1}-j_{l}, n)%$. Based on the result, necessary and sufficient conditions are given to decide whether a circulant digraph is antistrong, weakly-antistrong or anti-Eulerian. | ||
| 650 | 4 | |a Antistrong |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Weakly-antistrong |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Bi-Circulant graph |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Circulant digraph |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Anti-Eulerian |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Meng, Jixiang |0 (orcid)0000-0001-6853-8163 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Graphs and combinatorics |d Tokyo : Springer-Verl. Tokyo, 1985 |g 39(2023), 2 vom: 16. Feb. |w (DE-627)30018381X |w (DE-600)1481435-3 |x 1435-5914 |7 nnns |
| 773 | 1 | 8 | |g volume:39 |g year:2023 |g number:2 |g day:16 |g month:02 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s00373-023-02620-4 |z lizenzpflichtig |3 Volltext |
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10.1007/s00373-023-02620-4 doi (DE-627)SPR049348876 (SPR)s00373-023-02620-4-e DE-627 ger DE-627 rakwb eng Yuan, Lili verfasserin aut Necessary and Sufficient Conditions for Circulant Digraphs to be Antistrong, Weakly-Antistrong and Anti-Eulerian 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract An antidirected trail in a digraph is a trail (a walk with no arc repeated) in which the consecutive arcs have opposite directions. The forward antidirected trails are special antidirected trails which begin and end with forward arcs. A digraph D containing a forward antidirected (x, y)-trail for every choice of %$x,y\in V(D)%$ is called antistrong. An antidirected trail which begins with a forward arc and ends with a backward arc is a forward-backward antidirected trail. For any %$x,y\in V(D)%$, if digraph D has a forward antidirected (x, y)-trail or a forward-backward antidirected (x, y)-trail, then D is weakly-antistrong. A digraph is anti-Eulerian if it admits a closed anti-directed Euler trail. Let %$BC(Z_n, C)%$ be a Bi-Circulant graph with %$n\ge 3%$ and %$C=\{j_1, j_2, \ldots , j_{l}\}%$, %$l\ge 2%$. This paper shows that the number of connected components of %$BC(Z_n, C)%$ is equal to %$gcd(j_1-j_l, \ldots , j_{l-1}-j_{l}, n)%$. Based on the result, necessary and sufficient conditions are given to decide whether a circulant digraph is antistrong, weakly-antistrong or anti-Eulerian. Antistrong (dpeaa)DE-He213 Weakly-antistrong (dpeaa)DE-He213 Bi-Circulant graph (dpeaa)DE-He213 Circulant digraph (dpeaa)DE-He213 Anti-Eulerian (dpeaa)DE-He213 Meng, Jixiang (orcid)0000-0001-6853-8163 aut Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 39(2023), 2 vom: 16. Feb. (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:39 year:2023 number:2 day:16 month:02 https://dx.doi.org/10.1007/s00373-023-02620-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 2 16 02 |
| spelling |
10.1007/s00373-023-02620-4 doi (DE-627)SPR049348876 (SPR)s00373-023-02620-4-e DE-627 ger DE-627 rakwb eng Yuan, Lili verfasserin aut Necessary and Sufficient Conditions for Circulant Digraphs to be Antistrong, Weakly-Antistrong and Anti-Eulerian 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract An antidirected trail in a digraph is a trail (a walk with no arc repeated) in which the consecutive arcs have opposite directions. The forward antidirected trails are special antidirected trails which begin and end with forward arcs. A digraph D containing a forward antidirected (x, y)-trail for every choice of %$x,y\in V(D)%$ is called antistrong. An antidirected trail which begins with a forward arc and ends with a backward arc is a forward-backward antidirected trail. For any %$x,y\in V(D)%$, if digraph D has a forward antidirected (x, y)-trail or a forward-backward antidirected (x, y)-trail, then D is weakly-antistrong. A digraph is anti-Eulerian if it admits a closed anti-directed Euler trail. Let %$BC(Z_n, C)%$ be a Bi-Circulant graph with %$n\ge 3%$ and %$C=\{j_1, j_2, \ldots , j_{l}\}%$, %$l\ge 2%$. This paper shows that the number of connected components of %$BC(Z_n, C)%$ is equal to %$gcd(j_1-j_l, \ldots , j_{l-1}-j_{l}, n)%$. Based on the result, necessary and sufficient conditions are given to decide whether a circulant digraph is antistrong, weakly-antistrong or anti-Eulerian. Antistrong (dpeaa)DE-He213 Weakly-antistrong (dpeaa)DE-He213 Bi-Circulant graph (dpeaa)DE-He213 Circulant digraph (dpeaa)DE-He213 Anti-Eulerian (dpeaa)DE-He213 Meng, Jixiang (orcid)0000-0001-6853-8163 aut Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 39(2023), 2 vom: 16. Feb. (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:39 year:2023 number:2 day:16 month:02 https://dx.doi.org/10.1007/s00373-023-02620-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 2 16 02 |
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10.1007/s00373-023-02620-4 doi (DE-627)SPR049348876 (SPR)s00373-023-02620-4-e DE-627 ger DE-627 rakwb eng Yuan, Lili verfasserin aut Necessary and Sufficient Conditions for Circulant Digraphs to be Antistrong, Weakly-Antistrong and Anti-Eulerian 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract An antidirected trail in a digraph is a trail (a walk with no arc repeated) in which the consecutive arcs have opposite directions. The forward antidirected trails are special antidirected trails which begin and end with forward arcs. A digraph D containing a forward antidirected (x, y)-trail for every choice of %$x,y\in V(D)%$ is called antistrong. An antidirected trail which begins with a forward arc and ends with a backward arc is a forward-backward antidirected trail. For any %$x,y\in V(D)%$, if digraph D has a forward antidirected (x, y)-trail or a forward-backward antidirected (x, y)-trail, then D is weakly-antistrong. A digraph is anti-Eulerian if it admits a closed anti-directed Euler trail. Let %$BC(Z_n, C)%$ be a Bi-Circulant graph with %$n\ge 3%$ and %$C=\{j_1, j_2, \ldots , j_{l}\}%$, %$l\ge 2%$. This paper shows that the number of connected components of %$BC(Z_n, C)%$ is equal to %$gcd(j_1-j_l, \ldots , j_{l-1}-j_{l}, n)%$. Based on the result, necessary and sufficient conditions are given to decide whether a circulant digraph is antistrong, weakly-antistrong or anti-Eulerian. Antistrong (dpeaa)DE-He213 Weakly-antistrong (dpeaa)DE-He213 Bi-Circulant graph (dpeaa)DE-He213 Circulant digraph (dpeaa)DE-He213 Anti-Eulerian (dpeaa)DE-He213 Meng, Jixiang (orcid)0000-0001-6853-8163 aut Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 39(2023), 2 vom: 16. Feb. (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:39 year:2023 number:2 day:16 month:02 https://dx.doi.org/10.1007/s00373-023-02620-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 2 16 02 |
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10.1007/s00373-023-02620-4 doi (DE-627)SPR049348876 (SPR)s00373-023-02620-4-e DE-627 ger DE-627 rakwb eng Yuan, Lili verfasserin aut Necessary and Sufficient Conditions for Circulant Digraphs to be Antistrong, Weakly-Antistrong and Anti-Eulerian 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract An antidirected trail in a digraph is a trail (a walk with no arc repeated) in which the consecutive arcs have opposite directions. The forward antidirected trails are special antidirected trails which begin and end with forward arcs. A digraph D containing a forward antidirected (x, y)-trail for every choice of %$x,y\in V(D)%$ is called antistrong. An antidirected trail which begins with a forward arc and ends with a backward arc is a forward-backward antidirected trail. For any %$x,y\in V(D)%$, if digraph D has a forward antidirected (x, y)-trail or a forward-backward antidirected (x, y)-trail, then D is weakly-antistrong. A digraph is anti-Eulerian if it admits a closed anti-directed Euler trail. Let %$BC(Z_n, C)%$ be a Bi-Circulant graph with %$n\ge 3%$ and %$C=\{j_1, j_2, \ldots , j_{l}\}%$, %$l\ge 2%$. This paper shows that the number of connected components of %$BC(Z_n, C)%$ is equal to %$gcd(j_1-j_l, \ldots , j_{l-1}-j_{l}, n)%$. Based on the result, necessary and sufficient conditions are given to decide whether a circulant digraph is antistrong, weakly-antistrong or anti-Eulerian. Antistrong (dpeaa)DE-He213 Weakly-antistrong (dpeaa)DE-He213 Bi-Circulant graph (dpeaa)DE-He213 Circulant digraph (dpeaa)DE-He213 Anti-Eulerian (dpeaa)DE-He213 Meng, Jixiang (orcid)0000-0001-6853-8163 aut Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 39(2023), 2 vom: 16. Feb. (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:39 year:2023 number:2 day:16 month:02 https://dx.doi.org/10.1007/s00373-023-02620-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 2 16 02 |
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10.1007/s00373-023-02620-4 doi (DE-627)SPR049348876 (SPR)s00373-023-02620-4-e DE-627 ger DE-627 rakwb eng Yuan, Lili verfasserin aut Necessary and Sufficient Conditions for Circulant Digraphs to be Antistrong, Weakly-Antistrong and Anti-Eulerian 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract An antidirected trail in a digraph is a trail (a walk with no arc repeated) in which the consecutive arcs have opposite directions. The forward antidirected trails are special antidirected trails which begin and end with forward arcs. A digraph D containing a forward antidirected (x, y)-trail for every choice of %$x,y\in V(D)%$ is called antistrong. An antidirected trail which begins with a forward arc and ends with a backward arc is a forward-backward antidirected trail. For any %$x,y\in V(D)%$, if digraph D has a forward antidirected (x, y)-trail or a forward-backward antidirected (x, y)-trail, then D is weakly-antistrong. A digraph is anti-Eulerian if it admits a closed anti-directed Euler trail. Let %$BC(Z_n, C)%$ be a Bi-Circulant graph with %$n\ge 3%$ and %$C=\{j_1, j_2, \ldots , j_{l}\}%$, %$l\ge 2%$. This paper shows that the number of connected components of %$BC(Z_n, C)%$ is equal to %$gcd(j_1-j_l, \ldots , j_{l-1}-j_{l}, n)%$. Based on the result, necessary and sufficient conditions are given to decide whether a circulant digraph is antistrong, weakly-antistrong or anti-Eulerian. Antistrong (dpeaa)DE-He213 Weakly-antistrong (dpeaa)DE-He213 Bi-Circulant graph (dpeaa)DE-He213 Circulant digraph (dpeaa)DE-He213 Anti-Eulerian (dpeaa)DE-He213 Meng, Jixiang (orcid)0000-0001-6853-8163 aut Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 39(2023), 2 vom: 16. Feb. (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:39 year:2023 number:2 day:16 month:02 https://dx.doi.org/10.1007/s00373-023-02620-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 2 16 02 |
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract An antidirected trail in a digraph is a trail (a walk with no arc repeated) in which the consecutive arcs have opposite directions. The forward antidirected trails are special antidirected trails which begin and end with forward arcs. A digraph D containing a forward antidirected (x, y)-trail for every choice of %$x,y\in V(D)%$ is called antistrong. An antidirected trail which begins with a forward arc and ends with a backward arc is a forward-backward antidirected trail. For any %$x,y\in V(D)%$, if digraph D has a forward antidirected (x, y)-trail or a forward-backward antidirected (x, y)-trail, then D is weakly-antistrong. A digraph is anti-Eulerian if it admits a closed anti-directed Euler trail. Let %$BC(Z_n, C)%$ be a Bi-Circulant graph with %$n\ge 3%$ and %$C=\{j_1, j_2, \ldots , j_{l}\}%$, %$l\ge 2%$. This paper shows that the number of connected components of %$BC(Z_n, C)%$ is equal to %$gcd(j_1-j_l, \ldots , j_{l-1}-j_{l}, n)%$. 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Yuan, Lili |
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Yuan, Lili misc Antistrong misc Weakly-antistrong misc Bi-Circulant graph misc Circulant digraph misc Anti-Eulerian Necessary and Sufficient Conditions for Circulant Digraphs to be Antistrong, Weakly-Antistrong and Anti-Eulerian |
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Necessary and Sufficient Conditions for Circulant Digraphs to be Antistrong, Weakly-Antistrong and Anti-Eulerian Antistrong (dpeaa)DE-He213 Weakly-antistrong (dpeaa)DE-He213 Bi-Circulant graph (dpeaa)DE-He213 Circulant digraph (dpeaa)DE-He213 Anti-Eulerian (dpeaa)DE-He213 |
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misc Antistrong misc Weakly-antistrong misc Bi-Circulant graph misc Circulant digraph misc Anti-Eulerian |
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misc Antistrong misc Weakly-antistrong misc Bi-Circulant graph misc Circulant digraph misc Anti-Eulerian |
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Necessary and Sufficient Conditions for Circulant Digraphs to be Antistrong, Weakly-Antistrong and Anti-Eulerian |
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Necessary and Sufficient Conditions for Circulant Digraphs to be Antistrong, Weakly-Antistrong and Anti-Eulerian |
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necessary and sufficient conditions for circulant digraphs to be antistrong, weakly-antistrong and anti-eulerian |
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Necessary and Sufficient Conditions for Circulant Digraphs to be Antistrong, Weakly-Antistrong and Anti-Eulerian |
| abstract |
Abstract An antidirected trail in a digraph is a trail (a walk with no arc repeated) in which the consecutive arcs have opposite directions. The forward antidirected trails are special antidirected trails which begin and end with forward arcs. A digraph D containing a forward antidirected (x, y)-trail for every choice of %$x,y\in V(D)%$ is called antistrong. An antidirected trail which begins with a forward arc and ends with a backward arc is a forward-backward antidirected trail. For any %$x,y\in V(D)%$, if digraph D has a forward antidirected (x, y)-trail or a forward-backward antidirected (x, y)-trail, then D is weakly-antistrong. A digraph is anti-Eulerian if it admits a closed anti-directed Euler trail. Let %$BC(Z_n, C)%$ be a Bi-Circulant graph with %$n\ge 3%$ and %$C=\{j_1, j_2, \ldots , j_{l}\}%$, %$l\ge 2%$. This paper shows that the number of connected components of %$BC(Z_n, C)%$ is equal to %$gcd(j_1-j_l, \ldots , j_{l-1}-j_{l}, n)%$. Based on the result, necessary and sufficient conditions are given to decide whether a circulant digraph is antistrong, weakly-antistrong or anti-Eulerian. © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstractGer |
Abstract An antidirected trail in a digraph is a trail (a walk with no arc repeated) in which the consecutive arcs have opposite directions. The forward antidirected trails are special antidirected trails which begin and end with forward arcs. A digraph D containing a forward antidirected (x, y)-trail for every choice of %$x,y\in V(D)%$ is called antistrong. An antidirected trail which begins with a forward arc and ends with a backward arc is a forward-backward antidirected trail. For any %$x,y\in V(D)%$, if digraph D has a forward antidirected (x, y)-trail or a forward-backward antidirected (x, y)-trail, then D is weakly-antistrong. A digraph is anti-Eulerian if it admits a closed anti-directed Euler trail. Let %$BC(Z_n, C)%$ be a Bi-Circulant graph with %$n\ge 3%$ and %$C=\{j_1, j_2, \ldots , j_{l}\}%$, %$l\ge 2%$. This paper shows that the number of connected components of %$BC(Z_n, C)%$ is equal to %$gcd(j_1-j_l, \ldots , j_{l-1}-j_{l}, n)%$. Based on the result, necessary and sufficient conditions are given to decide whether a circulant digraph is antistrong, weakly-antistrong or anti-Eulerian. © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstract_unstemmed |
Abstract An antidirected trail in a digraph is a trail (a walk with no arc repeated) in which the consecutive arcs have opposite directions. The forward antidirected trails are special antidirected trails which begin and end with forward arcs. A digraph D containing a forward antidirected (x, y)-trail for every choice of %$x,y\in V(D)%$ is called antistrong. An antidirected trail which begins with a forward arc and ends with a backward arc is a forward-backward antidirected trail. For any %$x,y\in V(D)%$, if digraph D has a forward antidirected (x, y)-trail or a forward-backward antidirected (x, y)-trail, then D is weakly-antistrong. A digraph is anti-Eulerian if it admits a closed anti-directed Euler trail. Let %$BC(Z_n, C)%$ be a Bi-Circulant graph with %$n\ge 3%$ and %$C=\{j_1, j_2, \ldots , j_{l}\}%$, %$l\ge 2%$. This paper shows that the number of connected components of %$BC(Z_n, C)%$ is equal to %$gcd(j_1-j_l, \ldots , j_{l-1}-j_{l}, n)%$. Based on the result, necessary and sufficient conditions are given to decide whether a circulant digraph is antistrong, weakly-antistrong or anti-Eulerian. © The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| title_short |
Necessary and Sufficient Conditions for Circulant Digraphs to be Antistrong, Weakly-Antistrong and Anti-Eulerian |
| url |
https://dx.doi.org/10.1007/s00373-023-02620-4 |
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| author2 |
Meng, Jixiang |
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Meng, Jixiang |
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10.1007/s00373-023-02620-4 |
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2024-07-04T00:26:57.397Z |
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| score |
7.3974285 |