Author : O. ejima , k. o. aremu , a. audu
Keyword : Inverse graphs, energy of graphs, eigenvalues, adjacency matrix, finite groups, graph of finite groups
Subject : Mathematics
Article Type : Original article (research)
DOI : https://doi.org/10.1186/s42787-020-00101-8
Article File : Full Text PDF
Abstract : Let (G, ∗) be a finite group and S = {x ∈ G|x = x−1} be a subset of G containing its non-self invertible elements. The inverse graph of G denoted by (G) is a graphwhose set of vertices coincides with G such that two distinct vertices x and y are adjacent if either x ∗ y ∈ S or y ∗ x ∈ S. In this paper, we study the energy of the dihedral and symmetric groups, we show that if G is a finite non-abelian group with exactly two non-self invertible elements, then the associated inverse graph (G) is never a complete bipartite graph. Furthermore, we establish the isomorphism between the inverse graphs of a subgroup Dp of the dihedral group Dn of order 2p and subgroup Sk of the symmetric groups Sn of order k! such that 2p = n! (p, n, k ≥ 3 and p, n, k ∈ Z + ).
Article by : Dr Ahmed Audu
Article add date : 2020-11-02
How to cite : O. ejima , k. o. aremu , a. audu. (2020-November-02). Energy of inverse graphs of dihedral and symmetric groups. retrieved from https://openacessjournal.com/abstract/340