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 …

In the last couple of decades, there has been a big upsurge of research on graphs defined
on algebraic structures (groups, rings, vector spaces, semigroups, and others). Much of this …

The reduced power graph ℛ 𝒫 (G) of a group G is the graph whose vertex set is the set of all
elements of G, and two vertices u and v are adjacent in ℛ 𝒫 (G) if and only if〈 u〉⊂〈 v〉 or〈 …

Given a finite group $ G $, the commuting graph of $ G $ is the simple graph whose vertex
set is $ G $, and two distinct vertices are adjacent if they commute. In this paper, we classify …

The power graph of a group G is a simple and undirected graph with vertex set G and two
distinct vertices are adjacent if one is a power of the other. In this article, we characterize …

TOPICS IN FINITE GROUPS: HOMOLOGY GROUPS, π-PRODUCT GRAPHS, WREATH
PRODUCTS AND CUSPIDAL CHARACTERS Page 1 TOPICS IN FINITE GROUPS: HOMOLOGY …

For a group G and X a subset of G the commuting graph of G on X, denoted by C (G, X) C (G,
X), is the graph whose vertex set is X with x, y ∈ X x, y∈ X joined by an edge if x ≠ yx≠ y …

For a group H and a non-empty subset Γ⊆ H, the commuting graph G= C (H, Γ) is the graph
with Γ as the vertex set and where any x, y∈ Γ are joined by an edge if x and y commute in …

arXiv:2412.12345v1 [math.GR] 16 Dec 2024 Page 1 arXiv:2412.12345v1 [math.GR] 16 Dec
2024 Critical groups and partitions of finite groups Daniela Bubboloni Dipartimento di …

Let $ G $ be a finite, non-abelian group of the form $ G= AN $, where $ A\leq G $ is abelian,
and $ N\trianglelefteq G $ is cyclic. We prove that the commuting graph $\Gamma (G) $ of …