Topological indices of non-commuting graph of dihedral groups

Authors

  • Nur Idayu Alimon Universiti Teknologi Malaysia
  • Nor Haniza Sarmin Universiti Teknologi Malaysia
  • Ahmad Erfanian Ferdowsi University of Mashhad

DOI:

https://doi.org/10.11113/mjfas.v14n0.1270

Keywords:

Edge-Wiener index, Zagreb index, non-commuting graph, dihedral group

Abstract

Assume  is a non-abelian group  A dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. The non-commuting graph of  denoted by  is the graph of vertex set  whose vertices are non-central elements, in which  is the center of  and two distinct vertices  and  are joined by an edge if and only if  In this paper, some topological indices of the non-commuting graph,  of the dihedral groups,  are presented. In order to determine the Edge-Wiener index, First Zagreb index and Second Zagreb index of the non-commuting graph,  of the dihedral groups,  previous results of some of the topological indices of non-commuting graph of finite group are used. Then, the non-commuting graphs of dihedral groups of different orders are found. Finally, the generalisation of Edge-Wiener index, First Zagreb index and Second Zagreb index of the non-commuting graphs of dihedral groups are determined.

Author Biographies

Nur Idayu Alimon, Universiti Teknologi Malaysia

Department of Mathematical Sciences, Faculty of Science

Nor Haniza Sarmin, Universiti Teknologi Malaysia

Department of Mathematical Sciences, Faculty of Science

Ahmad Erfanian, Ferdowsi University of Mashhad

Department of Pure Mathematics, Faculty of Mathematical Sciences

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Published

25-10-2018