THE RANDIĆ INDEX OF A POWER GRAPH

A power graph is a simple, connected graph defined on a finite group, which accepts the elements of the group as vertices and defines the adjacency relationship between two vertices as “if one vertex is a power of the other”. The concept of power graph was first introduced to the mathematical literature by Kelarev and Quinn in 2000 [1]. Later, with the article of Chakrabarty et al. in 2009, studies in the field of power graphs gained momentum [2]. Another important study that shapes the power graph field is the one conducted by Chattopadhyay et al. in 2018 [3]. In their study, the adjacency matrix of the power graph was redefined by considering the block matrix structure. On the other hand, the concept of the Randić index was introduced by Milan Randić in 1975 [4]. In his study, the Randić index concept was used to determine the degree of branching of the carbon atomic skeleton. Later, with the studies carried out 1990’s the concept of Randić index entered the mathematical literature and began to be used frequently in this field. In this study, bounds were obtained for the Randić index of power graphs by considering the concepts of maximum degree, minimum degree, and vertex energy.