Let G be a finite non-abelian group and Z(G) its center. We associate commuting graph $$\Gamma (G)$$ to G, whose vertex set is $$G\setminus Z(G)$$ two distinct vertices are adjacent if they commute. In this paper we prove that the of all groups has maximum degree bounded above by fixed $$k \in {\mathbb {N}}$$ finite. Also, characterize for which associated graphs have at most 4.

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 24 November 2020Accepted: 25 July 2021Published online: 23 2021Keywordsgraphs, fractional coloring, girth, triangle-free, RamseyAMS Subject Headings05C15Publication DataISSN (print): 0895-4801ISSN (online): 1095-7146Publisher: Society for Industrial and Applied Mathematic...