Cubic Graphs Admitting Vertex-Transitive Almost Simple Groups
Abstract Let %${\varGamma }%$ be a connected cubic graph admitting a vertex-transitive almost simple group G of automorphisms. In this paper, we study the normality of the socle T of G in the full automorphism group %$\text {Aut}({\varGamma })%$ of %${\varGamma } %$. It is proved that if T is not no...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Du, Jia-Li [verfasserIn] |
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E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2023 |
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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), 6 vom: 28. Okt. |
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| Übergeordnetes Werk: |
volume:39 ; year:2023 ; number:6 ; day:28 ; month:10 |
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| DOI / URN: |
10.1007/s00373-023-02716-x |
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| Katalog-ID: |
SPR053560485 |
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| 520 | |a Abstract Let %${\varGamma }%$ be a connected cubic graph admitting a vertex-transitive almost simple group G of automorphisms. In this paper, we study the normality of the socle T of G in the full automorphism group %$\text {Aut}({\varGamma })%$ of %${\varGamma } %$. It is proved that if T is not normal in %$\text {Aut}({\varGamma })%$, then %$T= \text {A}_{47}%$, %$\text {A}_{23}%$, %$\text {A}_{2^f-1}%$ with %$f\ge 3%$, or a simple group of Lie type of even characteristic with some exceptions. In particular, if %${\varGamma }%$ is arc-transitive and T is not normal in %$\text {Aut}({\varGamma })%$, then %${\varGamma } %$ is a Cayley graph on G, and %$(\text {Aut}({\varGamma }),G)=(\text {A}_{48},\text {A}_{47})%$ or %$(\text {S}_{24},\text {S}_{23})%$. | ||
| 650 | 4 | |a Vertex-transitive graph |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Cubic graph, almost simple group |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Yin, Fu-Gang |0 (orcid)0000-0001-8328-0690 |4 aut | |
| 700 | 1 | |a Ding, Menglin |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Graphs and combinatorics |d Tokyo : Springer-Verl. Tokyo, 1985 |g 39(2023), 6 vom: 28. Okt. |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:6 |g day:28 |g month:10 |
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10.1007/s00373-023-02716-x doi (DE-627)SPR053560485 (SPR)s00373-023-02716-x-e DE-627 ger DE-627 rakwb eng Du, Jia-Li verfasserin aut Cubic Graphs Admitting Vertex-Transitive Almost Simple Groups 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 Let %${\varGamma }%$ be a connected cubic graph admitting a vertex-transitive almost simple group G of automorphisms. In this paper, we study the normality of the socle T of G in the full automorphism group %$\text {Aut}({\varGamma })%$ of %${\varGamma } %$. It is proved that if T is not normal in %$\text {Aut}({\varGamma })%$, then %$T= \text {A}_{47}%$, %$\text {A}_{23}%$, %$\text {A}_{2^f-1}%$ with %$f\ge 3%$, or a simple group of Lie type of even characteristic with some exceptions. In particular, if %${\varGamma }%$ is arc-transitive and T is not normal in %$\text {Aut}({\varGamma })%$, then %${\varGamma } %$ is a Cayley graph on G, and %$(\text {Aut}({\varGamma }),G)=(\text {A}_{48},\text {A}_{47})%$ or %$(\text {S}_{24},\text {S}_{23})%$. Vertex-transitive graph (dpeaa)DE-He213 Cubic graph, almost simple group (dpeaa)DE-He213 Yin, Fu-Gang (orcid)0000-0001-8328-0690 aut Ding, Menglin aut Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 39(2023), 6 vom: 28. Okt. (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:39 year:2023 number:6 day:28 month:10 https://dx.doi.org/10.1007/s00373-023-02716-x 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 6 28 10 |
| spelling |
10.1007/s00373-023-02716-x doi (DE-627)SPR053560485 (SPR)s00373-023-02716-x-e DE-627 ger DE-627 rakwb eng Du, Jia-Li verfasserin aut Cubic Graphs Admitting Vertex-Transitive Almost Simple Groups 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 Let %${\varGamma }%$ be a connected cubic graph admitting a vertex-transitive almost simple group G of automorphisms. In this paper, we study the normality of the socle T of G in the full automorphism group %$\text {Aut}({\varGamma })%$ of %${\varGamma } %$. It is proved that if T is not normal in %$\text {Aut}({\varGamma })%$, then %$T= \text {A}_{47}%$, %$\text {A}_{23}%$, %$\text {A}_{2^f-1}%$ with %$f\ge 3%$, or a simple group of Lie type of even characteristic with some exceptions. In particular, if %${\varGamma }%$ is arc-transitive and T is not normal in %$\text {Aut}({\varGamma })%$, then %${\varGamma } %$ is a Cayley graph on G, and %$(\text {Aut}({\varGamma }),G)=(\text {A}_{48},\text {A}_{47})%$ or %$(\text {S}_{24},\text {S}_{23})%$. Vertex-transitive graph (dpeaa)DE-He213 Cubic graph, almost simple group (dpeaa)DE-He213 Yin, Fu-Gang (orcid)0000-0001-8328-0690 aut Ding, Menglin aut Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 39(2023), 6 vom: 28. Okt. (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:39 year:2023 number:6 day:28 month:10 https://dx.doi.org/10.1007/s00373-023-02716-x 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 6 28 10 |
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10.1007/s00373-023-02716-x doi (DE-627)SPR053560485 (SPR)s00373-023-02716-x-e DE-627 ger DE-627 rakwb eng Du, Jia-Li verfasserin aut Cubic Graphs Admitting Vertex-Transitive Almost Simple Groups 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 Let %${\varGamma }%$ be a connected cubic graph admitting a vertex-transitive almost simple group G of automorphisms. In this paper, we study the normality of the socle T of G in the full automorphism group %$\text {Aut}({\varGamma })%$ of %${\varGamma } %$. It is proved that if T is not normal in %$\text {Aut}({\varGamma })%$, then %$T= \text {A}_{47}%$, %$\text {A}_{23}%$, %$\text {A}_{2^f-1}%$ with %$f\ge 3%$, or a simple group of Lie type of even characteristic with some exceptions. In particular, if %${\varGamma }%$ is arc-transitive and T is not normal in %$\text {Aut}({\varGamma })%$, then %${\varGamma } %$ is a Cayley graph on G, and %$(\text {Aut}({\varGamma }),G)=(\text {A}_{48},\text {A}_{47})%$ or %$(\text {S}_{24},\text {S}_{23})%$. Vertex-transitive graph (dpeaa)DE-He213 Cubic graph, almost simple group (dpeaa)DE-He213 Yin, Fu-Gang (orcid)0000-0001-8328-0690 aut Ding, Menglin aut Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 39(2023), 6 vom: 28. Okt. (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:39 year:2023 number:6 day:28 month:10 https://dx.doi.org/10.1007/s00373-023-02716-x 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 6 28 10 |
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10.1007/s00373-023-02716-x doi (DE-627)SPR053560485 (SPR)s00373-023-02716-x-e DE-627 ger DE-627 rakwb eng Du, Jia-Li verfasserin aut Cubic Graphs Admitting Vertex-Transitive Almost Simple Groups 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 Let %${\varGamma }%$ be a connected cubic graph admitting a vertex-transitive almost simple group G of automorphisms. In this paper, we study the normality of the socle T of G in the full automorphism group %$\text {Aut}({\varGamma })%$ of %${\varGamma } %$. It is proved that if T is not normal in %$\text {Aut}({\varGamma })%$, then %$T= \text {A}_{47}%$, %$\text {A}_{23}%$, %$\text {A}_{2^f-1}%$ with %$f\ge 3%$, or a simple group of Lie type of even characteristic with some exceptions. In particular, if %${\varGamma }%$ is arc-transitive and T is not normal in %$\text {Aut}({\varGamma })%$, then %${\varGamma } %$ is a Cayley graph on G, and %$(\text {Aut}({\varGamma }),G)=(\text {A}_{48},\text {A}_{47})%$ or %$(\text {S}_{24},\text {S}_{23})%$. Vertex-transitive graph (dpeaa)DE-He213 Cubic graph, almost simple group (dpeaa)DE-He213 Yin, Fu-Gang (orcid)0000-0001-8328-0690 aut Ding, Menglin aut Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 39(2023), 6 vom: 28. Okt. (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:39 year:2023 number:6 day:28 month:10 https://dx.doi.org/10.1007/s00373-023-02716-x 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 6 28 10 |
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10.1007/s00373-023-02716-x doi (DE-627)SPR053560485 (SPR)s00373-023-02716-x-e DE-627 ger DE-627 rakwb eng Du, Jia-Li verfasserin aut Cubic Graphs Admitting Vertex-Transitive Almost Simple Groups 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 Let %${\varGamma }%$ be a connected cubic graph admitting a vertex-transitive almost simple group G of automorphisms. In this paper, we study the normality of the socle T of G in the full automorphism group %$\text {Aut}({\varGamma })%$ of %${\varGamma } %$. It is proved that if T is not normal in %$\text {Aut}({\varGamma })%$, then %$T= \text {A}_{47}%$, %$\text {A}_{23}%$, %$\text {A}_{2^f-1}%$ with %$f\ge 3%$, or a simple group of Lie type of even characteristic with some exceptions. In particular, if %${\varGamma }%$ is arc-transitive and T is not normal in %$\text {Aut}({\varGamma })%$, then %${\varGamma } %$ is a Cayley graph on G, and %$(\text {Aut}({\varGamma }),G)=(\text {A}_{48},\text {A}_{47})%$ or %$(\text {S}_{24},\text {S}_{23})%$. Vertex-transitive graph (dpeaa)DE-He213 Cubic graph, almost simple group (dpeaa)DE-He213 Yin, Fu-Gang (orcid)0000-0001-8328-0690 aut Ding, Menglin aut Enthalten in Graphs and combinatorics Tokyo : Springer-Verl. Tokyo, 1985 39(2023), 6 vom: 28. Okt. (DE-627)30018381X (DE-600)1481435-3 1435-5914 nnns volume:39 year:2023 number:6 day:28 month:10 https://dx.doi.org/10.1007/s00373-023-02716-x 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 6 28 10 |
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Enthalten in Graphs and combinatorics 39(2023), 6 vom: 28. Okt. volume:39 year:2023 number:6 day:28 month:10 |
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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 Let %${\varGamma }%$ be a connected cubic graph admitting a vertex-transitive almost simple group G of automorphisms. In this paper, we study the normality of the socle T of G in the full automorphism group %$\text {Aut}({\varGamma })%$ of %${\varGamma } %$. It is proved that if T is not normal in %$\text {Aut}({\varGamma })%$, then %$T= \text {A}_{47}%$, %$\text {A}_{23}%$, %$\text {A}_{2^f-1}%$ with %$f\ge 3%$, or a simple group of Lie type of even characteristic with some exceptions. 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Du, Jia-Li |
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Du, Jia-Li misc Vertex-transitive graph misc Cubic graph, almost simple group Cubic Graphs Admitting Vertex-Transitive Almost Simple Groups |
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Cubic Graphs Admitting Vertex-Transitive Almost Simple Groups Vertex-transitive graph (dpeaa)DE-He213 Cubic graph, almost simple group (dpeaa)DE-He213 |
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misc Vertex-transitive graph misc Cubic graph, almost simple group |
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cubic graphs admitting vertex-transitive almost simple groups |
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Cubic Graphs Admitting Vertex-Transitive Almost Simple Groups |
| abstract |
Abstract Let %${\varGamma }%$ be a connected cubic graph admitting a vertex-transitive almost simple group G of automorphisms. In this paper, we study the normality of the socle T of G in the full automorphism group %$\text {Aut}({\varGamma })%$ of %${\varGamma } %$. It is proved that if T is not normal in %$\text {Aut}({\varGamma })%$, then %$T= \text {A}_{47}%$, %$\text {A}_{23}%$, %$\text {A}_{2^f-1}%$ with %$f\ge 3%$, or a simple group of Lie type of even characteristic with some exceptions. In particular, if %${\varGamma }%$ is arc-transitive and T is not normal in %$\text {Aut}({\varGamma })%$, then %${\varGamma } %$ is a Cayley graph on G, and %$(\text {Aut}({\varGamma }),G)=(\text {A}_{48},\text {A}_{47})%$ or %$(\text {S}_{24},\text {S}_{23})%$. © 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 Let %${\varGamma }%$ be a connected cubic graph admitting a vertex-transitive almost simple group G of automorphisms. In this paper, we study the normality of the socle T of G in the full automorphism group %$\text {Aut}({\varGamma })%$ of %${\varGamma } %$. It is proved that if T is not normal in %$\text {Aut}({\varGamma })%$, then %$T= \text {A}_{47}%$, %$\text {A}_{23}%$, %$\text {A}_{2^f-1}%$ with %$f\ge 3%$, or a simple group of Lie type of even characteristic with some exceptions. In particular, if %${\varGamma }%$ is arc-transitive and T is not normal in %$\text {Aut}({\varGamma })%$, then %${\varGamma } %$ is a Cayley graph on G, and %$(\text {Aut}({\varGamma }),G)=(\text {A}_{48},\text {A}_{47})%$ or %$(\text {S}_{24},\text {S}_{23})%$. © 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 Let %${\varGamma }%$ be a connected cubic graph admitting a vertex-transitive almost simple group G of automorphisms. In this paper, we study the normality of the socle T of G in the full automorphism group %$\text {Aut}({\varGamma })%$ of %${\varGamma } %$. It is proved that if T is not normal in %$\text {Aut}({\varGamma })%$, then %$T= \text {A}_{47}%$, %$\text {A}_{23}%$, %$\text {A}_{2^f-1}%$ with %$f\ge 3%$, or a simple group of Lie type of even characteristic with some exceptions. In particular, if %${\varGamma }%$ is arc-transitive and T is not normal in %$\text {Aut}({\varGamma })%$, then %${\varGamma } %$ is a Cayley graph on G, and %$(\text {Aut}({\varGamma }),G)=(\text {A}_{48},\text {A}_{47})%$ or %$(\text {S}_{24},\text {S}_{23})%$. © 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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6 |
| title_short |
Cubic Graphs Admitting Vertex-Transitive Almost Simple Groups |
| url |
https://dx.doi.org/10.1007/s00373-023-02716-x |
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true |
| author2 |
Yin, Fu-Gang Ding, Menglin |
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Yin, Fu-Gang Ding, Menglin |
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30018381X |
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| doi_str |
10.1007/s00373-023-02716-x |
| up_date |
2024-07-03T20:24:25.970Z |
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1803590844785098752 |
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| score |
7.400141 |