A completeness criterion for the common divisor graph on p -regular class sizes
Abstract
Let G be a finite group. For a fixed prime p, let Γp(G) be the common divisor graph built on the set of sizes of p-regular conjugacy classes of G: this is the simple undirected graph whose vertices are the class sizes of those non-central elements of G such that p does not divide their order, and two distinct vertices are adjacent if and only if they are not coprime. In this note we prove that if Γp(G) is a k-regular graph with k≥1, then it is a complete graph with k+1 vertices.
Fields of Study & Subjects
Finite Group Theory Research
Graph theory and applications
Advanced Graph Theory Research
Publication details
- Journal / source
- Communications in Algebra
- Pages
- 1–6
- Publication date
- 5 February 2026
- Language
- EN