{"paper":{"title":"Maximum-Size Independent Sets and Automorphism Groups of Tensor Powers of the Even Derangement Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Fu-Ji Xie, Xiao-Dong Zhang, Yun-Ping Deng","submitted_at":"2011-11-12T02:55:48Z","abstract_excerpt":"Let $A_n$ be the alternating group of even permutations of $X:=\\{1,2,...,n\\}$ and ${\\mathcal E}_n$ the set of even derangements on $X.$ Denote by $A\\T_n^q$ the tensor product of $q$ copies of $A\\T_n,$ where the Cayley graph $A\\T_n:=\\T(A_n,{\\mathcal E}_n)$ is called the even derangement graph. In this paper, we intensively investigate the properties of $A\\T_n^q$ including connectedness, diameter, independence number, clique number, chromatic number and the maximum-size independent sets of $A\\T_n^q.$ By using the result on the maximum-size independent sets $A\\T_n^q$, we completely determine the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2895","kind":"arxiv","version":1},"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"}