{"paper":{"title":"Remarks on singular Cayley graphs and vanishing elements of simple groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexandre Zalesski, Johannes Siemons","submitted_at":"2018-04-04T01:18:18Z","abstract_excerpt":"Let $\\Gamma$ be a finite graph and let $A(\\Gamma)$ be its adjacency matrix. Then $\\Gamma$ is {\\it singular} if $A(\\Gamma)$ is singular. The singularity of graphs is of certain interest in graph theory and algebraic combinatorics. Here we investigate this problem for Cayley graphs ${\\rm Cay}(G,H)$ when $G$ is a finite group and when the connecting set $H$ is a union of conjugacy classes of $G.$ In this situation the singularity problem reduces to finding an irreducible character $\\chi$ of $G$ for which $\\sum_{h\\in H}\\,\\chi(h)=0.$\n  At this stage we focus on the case when $H$ is a single conjuga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01204","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"}