The First Zagreb Index, The Wiener Index, and The Gutman Index of The Power of Dihedral Group

Abstract

Research on graphs combined with groups is an interesting topic in the field of combinatoric algebra where graphs are used to represent a group. One type of graph representation of a group is a power graph. A power graph of the group G is defined as a graph whose vertex set is all elements of G and two distinct vertices a and b are adjacent if and only if  or  for a positive integer  and . In addition to mathematics, graph theory can be applied to various fields of science, one of which is chemistry, which is related to topological indices. In this study, the topological indexes will be discussed, namely the Zagreb index, the Wiener index, and the Gutman index of the power graph of the dihedral group  where  with  prime numbers and an  natural number. The method used in this research is a literature review. The results obtained from this study are the first Zagreb index, Wiener index, and Gutman index of the power graph of the dihedral group  where  where  is prime and an m natural number respectively is .