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### jzs-10846

Result Involution Graphs of Finite Groups

Asaad A. Jund1 , Haval M. Mohammed Salih1*

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

*Corresponding author's email: havalmahmood07@gmail.com

Original: 6 September 2020 Revised: 10 February 2021 Accepted: 2 March 202Published online:  20 June 2021

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.

.Keywords: Involution Element, Complete  Bipartite Graph, Girth and Diameter.

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