Intersection density of cubic symmetric graphs

Abstract Two elements g, h of a permutation group G acting on a set V are said to be intersecting if %$g(v) = h(v)%$ for some %$v \in V%$. More generally, a subset %$\mathcal {F}%$ of G is an intersecting set if every pair of elements of %$\mathcal {F}%$ is intersecting. The intersection density %$\...
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Autor*in:	Kutnar, Klavdija [verfasserIn] Marušič, Dragan Pujol, Cyril

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Intersecting set Intersection density Intersection density array Cubic symmetric graph Transitive permutation group

Anmerkung:	© The Author(s) 2023

Übergeordnetes Werk:	Enthalten in: Journal of algebraic combinatorics - Dordrecht [u.a.] : Springer Science + Business Media B.V., 1992, 57(2023), 4 vom: 03. Apr., Seite 1313-1326
Übergeordnetes Werk:	volume:57 ; year:2023 ; number:4 ; day:03 ; month:04 ; pages:1313-1326

Links:	Volltext

DOI / URN:	10.1007/s10801-023-01228-4

Katalog-ID:	SPR05242913X

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520			\|a Abstract Two elements g, h of a permutation group G acting on a set V are said to be intersecting if %$g(v) = h(v)%$ for some %$v \in V%$. More generally, a subset %$\mathcal {F}%$ of G is an intersecting set if every pair of elements of %$\mathcal {F}%$ is intersecting. The intersection density %$\rho (G)%$ of a transitive permutation group G is the maximum value of the quotient %$\|\mathcal {F}\|/\|G_v\|%$ where %$\mathcal {F}%$ runs over all intersecting sets in G and %$G_v%$ is the stabilizer of %$v \in V%$. A vertex-transitive graph X is intersection density stable if any two transitive subgroups of %${\textrm{Aut}}\,(X)%$ have the same intersection density. This paper studies the above concepts in the context of cubic symmetric graphs. While a 1-regular cubic symmetric graph is necessarily intersection density stable, the situation for 2-arc-regular cubic symmetric graphs is more complex. A necessary condition for a 2-arc-regular cubic symmetric graph admitting a 1-arc-regular subgroup of automorphisms to be intersection density stable is given, and an infinite family of such graphs is constructed.
650		4	\|a Intersecting set \|7 (dpeaa)DE-He213
650		4	\|a Intersection density \|7 (dpeaa)DE-He213
650		4	\|a Intersection density array \|7 (dpeaa)DE-He213
650		4	\|a Cubic symmetric graph \|7 (dpeaa)DE-He213
650		4	\|a Transitive permutation group \|7 (dpeaa)DE-He213
700	1		\|a Marušič, Dragan \|4 aut
700	1		\|a Pujol, Cyril \|4 aut
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856	4	0	\|u https://dx.doi.org/10.1007/s10801-023-01228-4 \|z kostenfrei \|3 Volltext
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912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4328
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
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allfields	10.1007/s10801-023-01228-4 doi (DE-627)SPR05242913X (SPR)s10801-023-01228-4-e DE-627 ger DE-627 rakwb eng Kutnar, Klavdija verfasserin aut Intersection density of cubic symmetric graphs 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract Two elements g, h of a permutation group G acting on a set V are said to be intersecting if %$g(v) = h(v)%$ for some %$v \in V%$. More generally, a subset %$\mathcal {F}%$ of G is an intersecting set if every pair of elements of %$\mathcal {F}%$ is intersecting. The intersection density %$\rho (G)%$ of a transitive permutation group G is the maximum value of the quotient %$\|\mathcal {F}\|/\|G_v\|%$ where %$\mathcal {F}%$ runs over all intersecting sets in G and %$G_v%$ is the stabilizer of %$v \in V%$. A vertex-transitive graph X is intersection density stable if any two transitive subgroups of %${\textrm{Aut}}\,(X)%$ have the same intersection density. This paper studies the above concepts in the context of cubic symmetric graphs. While a 1-regular cubic symmetric graph is necessarily intersection density stable, the situation for 2-arc-regular cubic symmetric graphs is more complex. A necessary condition for a 2-arc-regular cubic symmetric graph admitting a 1-arc-regular subgroup of automorphisms to be intersection density stable is given, and an infinite family of such graphs is constructed. Intersecting set (dpeaa)DE-He213 Intersection density (dpeaa)DE-He213 Intersection density array (dpeaa)DE-He213 Cubic symmetric graph (dpeaa)DE-He213 Transitive permutation group (dpeaa)DE-He213 Marušič, Dragan aut Pujol, Cyril aut Enthalten in Journal of algebraic combinatorics Dordrecht [u.a.] : Springer Science + Business Media B.V., 1992 57(2023), 4 vom: 03. Apr., Seite 1313-1326 (DE-627)271180722 (DE-600)1479499-8 1572-9192 nnns volume:57 year:2023 number:4 day:03 month:04 pages:1313-1326 https://dx.doi.org/10.1007/s10801-023-01228-4 kostenfrei 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_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_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 57 2023 4 03 04 1313-1326
spelling	10.1007/s10801-023-01228-4 doi (DE-627)SPR05242913X (SPR)s10801-023-01228-4-e DE-627 ger DE-627 rakwb eng Kutnar, Klavdija verfasserin aut Intersection density of cubic symmetric graphs 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract Two elements g, h of a permutation group G acting on a set V are said to be intersecting if %$g(v) = h(v)%$ for some %$v \in V%$. More generally, a subset %$\mathcal {F}%$ of G is an intersecting set if every pair of elements of %$\mathcal {F}%$ is intersecting. The intersection density %$\rho (G)%$ of a transitive permutation group G is the maximum value of the quotient %$\|\mathcal {F}\|/\|G_v\|%$ where %$\mathcal {F}%$ runs over all intersecting sets in G and %$G_v%$ is the stabilizer of %$v \in V%$. A vertex-transitive graph X is intersection density stable if any two transitive subgroups of %${\textrm{Aut}}\,(X)%$ have the same intersection density. This paper studies the above concepts in the context of cubic symmetric graphs. While a 1-regular cubic symmetric graph is necessarily intersection density stable, the situation for 2-arc-regular cubic symmetric graphs is more complex. A necessary condition for a 2-arc-regular cubic symmetric graph admitting a 1-arc-regular subgroup of automorphisms to be intersection density stable is given, and an infinite family of such graphs is constructed. Intersecting set (dpeaa)DE-He213 Intersection density (dpeaa)DE-He213 Intersection density array (dpeaa)DE-He213 Cubic symmetric graph (dpeaa)DE-He213 Transitive permutation group (dpeaa)DE-He213 Marušič, Dragan aut Pujol, Cyril aut Enthalten in Journal of algebraic combinatorics Dordrecht [u.a.] : Springer Science + Business Media B.V., 1992 57(2023), 4 vom: 03. Apr., Seite 1313-1326 (DE-627)271180722 (DE-600)1479499-8 1572-9192 nnns volume:57 year:2023 number:4 day:03 month:04 pages:1313-1326 https://dx.doi.org/10.1007/s10801-023-01228-4 kostenfrei 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_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_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 57 2023 4 03 04 1313-1326
allfields_unstemmed	10.1007/s10801-023-01228-4 doi (DE-627)SPR05242913X (SPR)s10801-023-01228-4-e DE-627 ger DE-627 rakwb eng Kutnar, Klavdija verfasserin aut Intersection density of cubic symmetric graphs 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract Two elements g, h of a permutation group G acting on a set V are said to be intersecting if %$g(v) = h(v)%$ for some %$v \in V%$. More generally, a subset %$\mathcal {F}%$ of G is an intersecting set if every pair of elements of %$\mathcal {F}%$ is intersecting. The intersection density %$\rho (G)%$ of a transitive permutation group G is the maximum value of the quotient %$\|\mathcal {F}\|/\|G_v\|%$ where %$\mathcal {F}%$ runs over all intersecting sets in G and %$G_v%$ is the stabilizer of %$v \in V%$. A vertex-transitive graph X is intersection density stable if any two transitive subgroups of %${\textrm{Aut}}\,(X)%$ have the same intersection density. This paper studies the above concepts in the context of cubic symmetric graphs. While a 1-regular cubic symmetric graph is necessarily intersection density stable, the situation for 2-arc-regular cubic symmetric graphs is more complex. A necessary condition for a 2-arc-regular cubic symmetric graph admitting a 1-arc-regular subgroup of automorphisms to be intersection density stable is given, and an infinite family of such graphs is constructed. Intersecting set (dpeaa)DE-He213 Intersection density (dpeaa)DE-He213 Intersection density array (dpeaa)DE-He213 Cubic symmetric graph (dpeaa)DE-He213 Transitive permutation group (dpeaa)DE-He213 Marušič, Dragan aut Pujol, Cyril aut Enthalten in Journal of algebraic combinatorics Dordrecht [u.a.] : Springer Science + Business Media B.V., 1992 57(2023), 4 vom: 03. Apr., Seite 1313-1326 (DE-627)271180722 (DE-600)1479499-8 1572-9192 nnns volume:57 year:2023 number:4 day:03 month:04 pages:1313-1326 https://dx.doi.org/10.1007/s10801-023-01228-4 kostenfrei 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_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_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 57 2023 4 03 04 1313-1326
allfieldsGer	10.1007/s10801-023-01228-4 doi (DE-627)SPR05242913X (SPR)s10801-023-01228-4-e DE-627 ger DE-627 rakwb eng Kutnar, Klavdija verfasserin aut Intersection density of cubic symmetric graphs 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract Two elements g, h of a permutation group G acting on a set V are said to be intersecting if %$g(v) = h(v)%$ for some %$v \in V%$. More generally, a subset %$\mathcal {F}%$ of G is an intersecting set if every pair of elements of %$\mathcal {F}%$ is intersecting. The intersection density %$\rho (G)%$ of a transitive permutation group G is the maximum value of the quotient %$\|\mathcal {F}\|/\|G_v\|%$ where %$\mathcal {F}%$ runs over all intersecting sets in G and %$G_v%$ is the stabilizer of %$v \in V%$. A vertex-transitive graph X is intersection density stable if any two transitive subgroups of %${\textrm{Aut}}\,(X)%$ have the same intersection density. This paper studies the above concepts in the context of cubic symmetric graphs. While a 1-regular cubic symmetric graph is necessarily intersection density stable, the situation for 2-arc-regular cubic symmetric graphs is more complex. A necessary condition for a 2-arc-regular cubic symmetric graph admitting a 1-arc-regular subgroup of automorphisms to be intersection density stable is given, and an infinite family of such graphs is constructed. Intersecting set (dpeaa)DE-He213 Intersection density (dpeaa)DE-He213 Intersection density array (dpeaa)DE-He213 Cubic symmetric graph (dpeaa)DE-He213 Transitive permutation group (dpeaa)DE-He213 Marušič, Dragan aut Pujol, Cyril aut Enthalten in Journal of algebraic combinatorics Dordrecht [u.a.] : Springer Science + Business Media B.V., 1992 57(2023), 4 vom: 03. Apr., Seite 1313-1326 (DE-627)271180722 (DE-600)1479499-8 1572-9192 nnns volume:57 year:2023 number:4 day:03 month:04 pages:1313-1326 https://dx.doi.org/10.1007/s10801-023-01228-4 kostenfrei 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_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_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 57 2023 4 03 04 1313-1326
allfieldsSound	10.1007/s10801-023-01228-4 doi (DE-627)SPR05242913X (SPR)s10801-023-01228-4-e DE-627 ger DE-627 rakwb eng Kutnar, Klavdija verfasserin aut Intersection density of cubic symmetric graphs 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract Two elements g, h of a permutation group G acting on a set V are said to be intersecting if %$g(v) = h(v)%$ for some %$v \in V%$. More generally, a subset %$\mathcal {F}%$ of G is an intersecting set if every pair of elements of %$\mathcal {F}%$ is intersecting. The intersection density %$\rho (G)%$ of a transitive permutation group G is the maximum value of the quotient %$\|\mathcal {F}\|/\|G_v\|%$ where %$\mathcal {F}%$ runs over all intersecting sets in G and %$G_v%$ is the stabilizer of %$v \in V%$. A vertex-transitive graph X is intersection density stable if any two transitive subgroups of %${\textrm{Aut}}\,(X)%$ have the same intersection density. This paper studies the above concepts in the context of cubic symmetric graphs. While a 1-regular cubic symmetric graph is necessarily intersection density stable, the situation for 2-arc-regular cubic symmetric graphs is more complex. A necessary condition for a 2-arc-regular cubic symmetric graph admitting a 1-arc-regular subgroup of automorphisms to be intersection density stable is given, and an infinite family of such graphs is constructed. Intersecting set (dpeaa)DE-He213 Intersection density (dpeaa)DE-He213 Intersection density array (dpeaa)DE-He213 Cubic symmetric graph (dpeaa)DE-He213 Transitive permutation group (dpeaa)DE-He213 Marušič, Dragan aut Pujol, Cyril aut Enthalten in Journal of algebraic combinatorics Dordrecht [u.a.] : Springer Science + Business Media B.V., 1992 57(2023), 4 vom: 03. Apr., Seite 1313-1326 (DE-627)271180722 (DE-600)1479499-8 1572-9192 nnns volume:57 year:2023 number:4 day:03 month:04 pages:1313-1326 https://dx.doi.org/10.1007/s10801-023-01228-4 kostenfrei 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_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_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 57 2023 4 03 04 1313-1326
language	English
source	Enthalten in Journal of algebraic combinatorics 57(2023), 4 vom: 03. Apr., Seite 1313-1326 volume:57 year:2023 number:4 day:03 month:04 pages:1313-1326
sourceStr	Enthalten in Journal of algebraic combinatorics 57(2023), 4 vom: 03. Apr., Seite 1313-1326 volume:57 year:2023 number:4 day:03 month:04 pages:1313-1326
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Intersecting set Intersection density Intersection density array Cubic symmetric graph Transitive permutation group
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container_title	Journal of algebraic combinatorics
authorswithroles_txt_mv	Kutnar, Klavdija @@aut@@ Marušič, Dragan @@aut@@ Pujol, Cyril @@aut@@
publishDateDaySort_date	2023-04-03T00:00:00Z
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language_de	englisch
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More generally, a subset %$\mathcal {F}%$ of G is an intersecting set if every pair of elements of %$\mathcal {F}%$ is intersecting. The intersection density %$\rho (G)%$ of a transitive permutation group G is the maximum value of the quotient %$\|\mathcal {F}\|/\|G_v\|%$ where %$\mathcal {F}%$ runs over all intersecting sets in G and %$G_v%$ is the stabilizer of %$v \in V%$. A vertex-transitive graph X is intersection density stable if any two transitive subgroups of %${\textrm{Aut}}\,(X)%$ have the same intersection density. This paper studies the above concepts in the context of cubic symmetric graphs. While a 1-regular cubic symmetric graph is necessarily intersection density stable, the situation for 2-arc-regular cubic symmetric graphs is more complex. 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author	Kutnar, Klavdija
spellingShingle	Kutnar, Klavdija misc Intersecting set misc Intersection density misc Intersection density array misc Cubic symmetric graph misc Transitive permutation group Intersection density of cubic symmetric graphs
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topic_title	Intersection density of cubic symmetric graphs Intersecting set (dpeaa)DE-He213 Intersection density (dpeaa)DE-He213 Intersection density array (dpeaa)DE-He213 Cubic symmetric graph (dpeaa)DE-He213 Transitive permutation group (dpeaa)DE-He213
topic	misc Intersecting set misc Intersection density misc Intersection density array misc Cubic symmetric graph misc Transitive permutation group
topic_unstemmed	misc Intersecting set misc Intersection density misc Intersection density array misc Cubic symmetric graph misc Transitive permutation group
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title_sort	intersection density of cubic symmetric graphs
title_auth	Intersection density of cubic symmetric graphs
abstract	Abstract Two elements g, h of a permutation group G acting on a set V are said to be intersecting if %$g(v) = h(v)%$ for some %$v \in V%$. More generally, a subset %$\mathcal {F}%$ of G is an intersecting set if every pair of elements of %$\mathcal {F}%$ is intersecting. The intersection density %$\rho (G)%$ of a transitive permutation group G is the maximum value of the quotient %$\|\mathcal {F}\|/\|G_v\|%$ where %$\mathcal {F}%$ runs over all intersecting sets in G and %$G_v%$ is the stabilizer of %$v \in V%$. A vertex-transitive graph X is intersection density stable if any two transitive subgroups of %${\textrm{Aut}}\,(X)%$ have the same intersection density. This paper studies the above concepts in the context of cubic symmetric graphs. While a 1-regular cubic symmetric graph is necessarily intersection density stable, the situation for 2-arc-regular cubic symmetric graphs is more complex. A necessary condition for a 2-arc-regular cubic symmetric graph admitting a 1-arc-regular subgroup of automorphisms to be intersection density stable is given, and an infinite family of such graphs is constructed. © The Author(s) 2023
abstractGer	Abstract Two elements g, h of a permutation group G acting on a set V are said to be intersecting if %$g(v) = h(v)%$ for some %$v \in V%$. More generally, a subset %$\mathcal {F}%$ of G is an intersecting set if every pair of elements of %$\mathcal {F}%$ is intersecting. The intersection density %$\rho (G)%$ of a transitive permutation group G is the maximum value of the quotient %$\|\mathcal {F}\|/\|G_v\|%$ where %$\mathcal {F}%$ runs over all intersecting sets in G and %$G_v%$ is the stabilizer of %$v \in V%$. A vertex-transitive graph X is intersection density stable if any two transitive subgroups of %${\textrm{Aut}}\,(X)%$ have the same intersection density. This paper studies the above concepts in the context of cubic symmetric graphs. While a 1-regular cubic symmetric graph is necessarily intersection density stable, the situation for 2-arc-regular cubic symmetric graphs is more complex. A necessary condition for a 2-arc-regular cubic symmetric graph admitting a 1-arc-regular subgroup of automorphisms to be intersection density stable is given, and an infinite family of such graphs is constructed. © The Author(s) 2023
abstract_unstemmed	Abstract Two elements g, h of a permutation group G acting on a set V are said to be intersecting if %$g(v) = h(v)%$ for some %$v \in V%$. More generally, a subset %$\mathcal {F}%$ of G is an intersecting set if every pair of elements of %$\mathcal {F}%$ is intersecting. The intersection density %$\rho (G)%$ of a transitive permutation group G is the maximum value of the quotient %$\|\mathcal {F}\|/\|G_v\|%$ where %$\mathcal {F}%$ runs over all intersecting sets in G and %$G_v%$ is the stabilizer of %$v \in V%$. A vertex-transitive graph X is intersection density stable if any two transitive subgroups of %${\textrm{Aut}}\,(X)%$ have the same intersection density. This paper studies the above concepts in the context of cubic symmetric graphs. While a 1-regular cubic symmetric graph is necessarily intersection density stable, the situation for 2-arc-regular cubic symmetric graphs is more complex. A necessary condition for a 2-arc-regular cubic symmetric graph admitting a 1-arc-regular subgroup of automorphisms to be intersection density stable is given, and an infinite family of such graphs is constructed. © The Author(s) 2023
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container_issue	4
title_short	Intersection density of cubic symmetric graphs
url	https://dx.doi.org/10.1007/s10801-023-01228-4
remote_bool	true
author2	Marušič, Dragan Pujol, Cyril
author2Str	Marušič, Dragan Pujol, Cyril
ppnlink	271180722
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isOA_txt	true
hochschulschrift_bool	false
doi_str	10.1007/s10801-023-01228-4
up_date	2024-07-04T02:46:26.350Z
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score	7.399829

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Intersection density of cubic symmetric graphs

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Zugang & Verfügbarkeit

Vorhandene Bände

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