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


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 \(CAG_n\).


Alternating group graph Cayley graph Second largest eigenvalue 

Mathematics Subject Classification




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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Authors and Affiliations

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

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