These notes concern aspects of various graphs whose vertex set is a group $ G $ and
whose edges reflect group structure in some way (so that they are invariant under the action …

Let S be a (multiplicative) commutative semigroup with 0. Associate to S a (simple) graph G
(S) with vertices the nonzero zero-divisors of S, and two distinct vertices x and y are adjacent …

The enhanced power graph 𝒢 e (G) of a group G is the graph with vertex set G such that two
vertices x and y are adjacent if they are contained in the same cyclic subgroup. We prove …

The commuting graph\varDelta (G) Δ (G) of a finite non-abelian group G is a simple graph
with vertex set G, and two distinct vertices x, y are adjacent if xy= yx xy= yx. In this paper, first …

Let Γ be a simple finite graph with vertex set V (Γ) and edge set E (Γ). Let R be an
equivalence relation on V (Γ). The R-super Γ graph Γ R is a simple graph with vertex set V …

The commuting graph of a finite non-commutative semigroup S, denoted G (S), is a simple
graph whose vertices are the non-central elements of S and two distinct vertices x, y are …

The commuting graph of a group G is the simple undirected graph whose vertices are the
non-central elements of G and two distinct vertices are adjacent if and only if they commute …

For an arbitrary set X (finite or infinite), denote by T (X) the semigroup of full transformations
on X. For α∈ T (X), let C (α)={β∈ T (X): αβ= βα} be the centralizer of α in T (X). The aim of …

A matrix ring with commuting graph of maximal diameter - ScienceDirect Skip to main
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For a finite group G, let B be an equivalence (equality, conjugacy or order) relation on G and
let A be a simple (power, enhanced power or commuting) graph with vertex set G. The B …