A Survey on Properties of Some Power Graphs

Algebraic graph theory explores the relationship between algebraic structures and graph theory. One significant area of study within this field is the investigation of power graphs derived from groups. In recent years, there has been substantial progress in understanding various aspects of power graphs, including their connectivity, spectral properties, isomorphism, automorphism, and characterization in terms of groups. A power graph is a type of graph derived from a mathematical structure, the power graph G(G) of a group G is a simple graph where the vertices represent the elements of the group, and two distinct vertices are adjacent if one is a power of the other. In this paper, our main objective is to provide a comprehensive survey focusing on the properties of enhanced power graphs, reduced power graphs. These variations of power graphs offer refined insights into the underlying group structure and its relationship with graph-theoretic properties.