Result Involution Graphs of Finite Groups

Volume 23 , Issue 1 , June 2021 , Pages 113-118

Authors

Asaad A. Jund 1 ; Haval M. Mohammed Salih 1

1 Soran University, Faculty of Science, Mathematics Department, Kawa St., Soran, Erbil, Iraq

DOI logo 10.17656/jzs.10846

Keywords

Abstract

In this paper, a new kind of graph on a finite group , namely the result involution graph is defined and studied. We use to denote this graph, is a simple undirected graph with vertex set.  Two distinct vertices are adjacent if and only if their product is nontrivial involution element in . The result involution graph for several finite groups are obtained. We study some properties of the result involution graph by resizing graph by using the conjugacy classes of . Finally, we show that the result involution graphs for the symmetric groups and the alternating groups are connected with diameter at most 3 and radius at most 2 for. Furthermore, they have girth 3.

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  • Published at20 June 2021

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