{"paper":{"title":"Groups all of whose undirected Cayley graphs are determined by their spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.SP"],"primary_cat":"math.CO","authors_text":"Alireza Abdollahi, Mojtaba Jazaeri, Shahrooz Janbaz","submitted_at":"2015-03-05T05:22:47Z","abstract_excerpt":"Let $G$ be a finite group, and $S$ be a subset of $G\\setminus\\{1\\}$ such that $S=S^{-1}$. Suppose that $Cay(G,S)$ is the Cayley graph on $G$ with respect to the set $S$ which is the graph whose vertex set is $G$ and two vertices $a,b\\in G$ are adjacent if and only if $ab^{-1}\\in S$. The adjacency spectrum $Spec(\\Gamma)$ of a graph $\\Gamma$ is the multiset of eigenvalues of its adjacency matrix. A graph $\\Gamma$ is called \"determined by its spectrum\" (or for short DS) whenever if a graph $\\Gamma'$ has the same spectrum as $\\Gamma$, then $\\Gamma \\cong \\Gamma'$. We say that the group $G$ is DS (C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01541","kind":"arxiv","version":3},"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"}