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 this book, we introduce several graphical representations of a ring. In the past three
decades, graphs constructed from algebraic structures have been studied extensively by …

Let $ G $ be a group. The\emph {power graph} of $ G $ is a graph with the vertex set $ G $,
having an edge between two elements whenever one is a power of the other. We …

A topological index is a number generated from a molecular structure (ie, a graph) that
indicates the essential structural properties of the proposed molecule. Indeed, it is an …

Abstract The COPRIME GRAPH GG with a FINITE GROUP G as follows: Take G as the
vertex set of GG and join two distinct vertices u and v if (| u|,| v|)= 1. In the paper, we explore …

The commuting graph of a group G, denoted by Γ (G), is a simple undirected graph whose
vertices are all non-central elements of G and two distinct vertices x, y are adjacent if xy= yx …

The power graph of a group G is a simple graph whose vertex-set is G and two vertices x
and y in G are adjacent if and only if one of them is a power of the other. The subgraph of is …

Abstract Let\(G\) be a group. The power graph\(\Gamma_P (G)\) of\(G\) is a graph with vertex
set\(V (\Gamma_P (G))= G\) and two distinct vertices\(x\) and\(y\) are adjacent in\(\Gamma_P …

The non-commuting graph ΓG of a non-abelian group G is defined as follows. The vertex set
of ΓG is G− Z (G) where Z (G) denotes the center of G and two vertices x and y are adjacent if …

In this paper, we initiate the study of spectrum of the commuting graphs of finite non-abelian
groups. We first compute the spectrum of this graph for several classes of finite groups, in …