{"paper":{"title":"Bounding the number of vertices in the degree graph of a finite group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Emanuele Pacifici, Lucia Sanus, Silvio Dolfi, Zeinab Akhlaghi","submitted_at":"2018-11-05T13:39:48Z","abstract_excerpt":"Let $G$ be a finite group, and let ${\\rm{cd}}(G)$ denote the set of degrees of the irreducible complex characters of $G$. The degree graph $\\Delta(G)$ of $G$ is defined as the simple undirected graph whose vertex set ${\\rm{V}}(G)$ consists of the prime divisors of the numbers in ${\\rm{cd}}(G)$, two distinct vertices $p$ and $q$ being adjacent if and only if $pq$ divides some number in ${\\rm{cd}}(G)$. In this note, we provide an upper bound on the size of ${\\rm{V}}(G)$ in terms of the clique number $\\omega(G)$ (i.e., the maximum size of a subset of ${\\rm{V}}(G)$ inducing a complete subgraph) of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01674","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"}