A 2-arc Transitive Hexavalent Nonnormal Cayley Graph on A<sub>119</sub>

A Cayley graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Γ</mo><mo>=</mo><mi mathvariant="sans-serif">Cay</mi><mo>(</mo><mi>G</m...

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Autores principales:	Bo Ling, Wanting Li, Bengong Lou
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	simple group nonnormal Cayley graph arc-transitive graph automorphism group Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/92ce701718704f7dac827029d361886d
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spelling	oai:doaj.org-article:92ce701718704f7dac827029d361886d2021-11-25T18:17:20ZA 2-arc Transitive Hexavalent Nonnormal Cayley Graph on A<sub>119</sub>10.3390/math92229352227-7390https://doaj.org/article/92ce701718704f7dac827029d361886d2021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2935https://doaj.org/toc/2227-7390A Cayley graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Γ</mo><mo>=</mo><mi mathvariant="sans-serif">Cay</mi><mo>(</mo><mi>G</mi><mo>,</mo><mi>S</mi><mo>)</mo></mrow></semantics></math></inline-formula> is said to be normal if the base group <i>G</i> is normal in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="sans-serif">Aut</mi><mo>Γ</mo></mrow></semantics></math></inline-formula>. The concept of the normality of Cayley graphs was first proposed by M.Y. Xu in 1998 and it plays a vital role in determining the full automorphism groups of Cayley graphs. In this paper, we construct an example of a 2-arc transitive hexavalent nonnormal Cayley graph on the alternating group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="sans-serif">A</mi><mn>119</mn></msub></semantics></math></inline-formula>. Furthermore, we determine the full automorphism group of this graph and show that it is isomorphic to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="sans-serif">A</mi><mn>120</mn></msub></semantics></math></inline-formula>.Bo LingWanting LiBengong LouMDPI AGarticlesimple groupnonnormal Cayley grapharc-transitive graphautomorphism groupMathematicsQA1-939ENMathematics, Vol 9, Iss 2935, p 2935 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	simple group nonnormal Cayley graph arc-transitive graph automorphism group Mathematics QA1-939
spellingShingle	simple group nonnormal Cayley graph arc-transitive graph automorphism group Mathematics QA1-939 Bo Ling Wanting Li Bengong Lou A 2-arc Transitive Hexavalent Nonnormal Cayley Graph on A<sub>119</sub>
description	A Cayley graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Γ</mo><mo>=</mo><mi mathvariant="sans-serif">Cay</mi><mo>(</mo><mi>G</mi><mo>,</mo><mi>S</mi><mo>)</mo></mrow></semantics></math></inline-formula> is said to be normal if the base group <i>G</i> is normal in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="sans-serif">Aut</mi><mo>Γ</mo></mrow></semantics></math></inline-formula>. The concept of the normality of Cayley graphs was first proposed by M.Y. Xu in 1998 and it plays a vital role in determining the full automorphism groups of Cayley graphs. In this paper, we construct an example of a 2-arc transitive hexavalent nonnormal Cayley graph on the alternating group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="sans-serif">A</mi><mn>119</mn></msub></semantics></math></inline-formula>. Furthermore, we determine the full automorphism group of this graph and show that it is isomorphic to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="sans-serif">A</mi><mn>120</mn></msub></semantics></math></inline-formula>.
format	article
author	Bo Ling Wanting Li Bengong Lou
author_facet	Bo Ling Wanting Li Bengong Lou
author_sort	Bo Ling
title	A 2-arc Transitive Hexavalent Nonnormal Cayley Graph on A<sub>119</sub>
title_short	A 2-arc Transitive Hexavalent Nonnormal Cayley Graph on A<sub>119</sub>
title_full	A 2-arc Transitive Hexavalent Nonnormal Cayley Graph on A<sub>119</sub>
title_fullStr	A 2-arc Transitive Hexavalent Nonnormal Cayley Graph on A<sub>119</sub>
title_full_unstemmed	A 2-arc Transitive Hexavalent Nonnormal Cayley Graph on A<sub>119</sub>
title_sort	2-arc transitive hexavalent nonnormal cayley graph on a<sub>119</sub>
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/92ce701718704f7dac827029d361886d
work_keys_str_mv	AT boling a2arctransitivehexavalentnonnormalcayleygraphonasub119sub AT wantingli a2arctransitivehexavalentnonnormalcayleygraphonasub119sub AT bengonglou a2arctransitivehexavalentnonnormalcayleygraphonasub119sub AT boling 2arctransitivehexavalentnonnormalcayleygraphonasub119sub AT wantingli 2arctransitivehexavalentnonnormalcayleygraphonasub119sub AT bengonglou 2arctransitivehexavalentnonnormalcayleygraphonasub119sub
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A 2-arc Transitive Hexavalent Nonnormal Cayley Graph on A<sub>119</sub>

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