{"paper":{"title":"The second largest eigenvalues of some Cayley graphs on alternating groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Qiongxiang Huang, Xueyi Huang","submitted_at":"2017-11-24T12:31:27Z","abstract_excerpt":"Let $A_n$ denote the alternating group of degree $n$ with $n\\geq 3$. 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 $T_1=\\{(1,2,i),(1,i,2)\\mid 3\\leq i\\leq n\\}$, $T_2=\\{(1,i,j),(1,j,i)\\mid 2\\leq i<j\\leq n\\}$ and $T_3=\\{(i,j,k),(i,k,j)\\mid 1\\leq i<j<k\\leq n\\}$. In this paper, we determine the second largest eigenvalues of $AG_n$, $EAG_n$ and $CAG_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08944","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}