Some Parameters of the Central Graphs of the Identity Graphs of Finite Cyclic Groups

Abstract

The interplay of groups and graphs has been a subject of interest by mathematics researchers nowadays. One particular instance is the identity graph of a group introduced by Kandasamy [5]. Moreover, the concept of a central graph of any graph is widely used by many graph theorists. The central graph of a graph G denoted by C(G) can be obtained by subdividing the edge of G exactly once and joining all the nonadjacent vertices of G in C(G). In this paper, we construct the central graph of the identity graph of finite cyclic group and investigate some of its graph properties.