Topological Indices of Relative g-noncommuting Graph of Dihedral Groups Nur Ain Supu (a) Intan Muchtadi Alamsyah ( a) Erma Suwastika (a*)
Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, 40132 Bandung, Indonesia
*ermasuwastika[at]itb.ac.id
Abstract
Let G be a finite group, H be a subgroup of G and g be a fixed element of G. The relative g-noncommuting graph \Gamma_{g,H,G} of G is defined as a graph with vertex set is G and two distinct vertices x and y are adjencent if [x,y]\neq g and [x,y]\neq g^{-1}, where at least x or y belong to H. In this paper, we will discuss the relative g-noncommuting graph of the dihedral groups D_{2n} in particular case when n is a prime number. We give several topological indices of the relative g-noncommuting graph of the dihedral groups D_{2n} including the first Zagreb index, Wiener index, Edge-Wiener index, Hyper-Wiener index, and Harary index.
Keywords: Relative g-noncommuting graph, Dihedral group, Topological indices
