The graph whose vertex set is W and such that two vertices are adjacent if and only if they are adjacent in G is called the subgraph of G induced by W .

We are interested in studying the regularity of Γ(G) and we con- jecture that, for every integer k ≥ 1, the graph Γ(G) cannot be regular unless it is a complete ...

May 25, 2020 · In this article we prove that, if \Gamma_G(N) is a connected incomplete regular graph, then N= P \times{A} where P is a p-group, for some prime p and A\leq{Z(G

Given a finite group GG, denote by Γ(G)Γ(G) the simple undirected graph whose vertices are the (distinct) non-central conjugacy class sizes of GG, ...

Oct 1, 2012 · In this note we prove that ( G ) is a 2 -regular graph if and only if it is a complete graph with three vertices, and ( G ) is a 3 -regular graph if and only ...

May 12, 2021 · We prove that, if ΓG(N) is a connected incomplete regular graph, then N=P×A where P is a p-group, for some prime p, A≤Z(G) and Z(N)≠N∩Z(G) .

TL;DR: In this article, it was shown that the prime graph Δ (G ) of a finite group G is 3-regular if and only if it is a complete graph with four vertices.

Given a finite group G, denote by Γ. (G) the simple undirected graph whose vertices are the (distinct) non-central conjugacy class sizes of G, and for which ...

Missing: regularity | Show results with:regularity

Missing: regularity | Show results with:regularity