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Journal of Algebraic Combinatorics

, Volume 50, Issue 1, pp 99–111 | Cite as

The second largest eigenvalues of some Cayley graphs on alternating groups

  • Xueyi Huang
  • Qiongxiang HuangEmail author
Article

Abstract

Let \(A_n\) denote the alternating group of degree n with \(n\ge 3\). The alternating group graph \(AG_n\), extended alternating group graph \(EAG_n\) and complete alternating group graph \(CAG_n\) are the Cayley graphs \(\mathrm {Cay}(A_n,T_1)\), \(\mathrm {Cay}(A_n,T_2)\) and \(\mathrm {Cay}(A_n,T_3)\), respectively, where \(T_1=\{(1,2,i),(1,i,2)\mid 3\le i\le n\}\), \(T_2=\{(1,i,j),(1,j,i)\mid 2\le i<j\le n\}\) and \(T_3=\{(i,j,k),(i,k,j)\mid 1\le i<j<k\le n\}\). In this paper, we determine the second largest eigenvalues of \(AG_n\), \(EAG_n\) and \(CAG_n\).

Keywords

Alternating group graph Cayley graph Second largest eigenvalue 

Mathematics Subject Classification

05C50 

Notes

Acknowledgements

The authors are grateful to the anonymous referees for their useful and constructive comments, which have considerably improved the presentation of this paper.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Mathematics and Systems ScienceXinjiang UniversityÜrümqiPeople’s Republic of China

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