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 …

Suppose G is a finite group. The power graph represented by P (G) of G is a graph, whose
node set is G, and two different elements are adjacent if and only if one is an integral power …

A survey on enhanced power graphs of finite groups Page 1 www.ejgta.org Electronic
Journal of Graph Theory and Applications 10 (1) (2022), 89–111 A survey on enhanced …

The difference graph D (G) of a finite group G is the difference of the enhanced power graph
of G and the power graph of G, where all isolated vertices are removed. In this paper we …

Molecular topology can be described by using topological indices. These are quantitative
measures of the essential structural features of a proposed molecule calculated from its …

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 study on graphs emerging from different algebraic structures such as groups, rings,
fields, vector spaces, etc. is a prominent area of research in mathematics, as algebra and …

This paper provides a bridge between two active areas of research, the spectrum (set of
element orders) and the power graph of a finite group. The order sequence of a finite group …

Let $ G $ be a group and $ L (G) $ be the set of all subgroups of $ G $. We introduce a
bipartite graph $\mathcal {B}(G) $ on $ G $ whose vertex set is the union of two sets …

Let G be a finite group and let P (G) be the undirected power graph of G. Recall that the
vertices of P (G) are labelled by the elements of G, with an edge between g 1 and g 2 if …