Construction of the <img src=image/13492345_01.gif> Graph of Mathieu Group <img src=image/13492345_02.gif>

Abstract

Suppose that <img src=image/13492345_03.gif> is a group and <img src=image/13492345_04.gif> is a subset of <img src=image/13492345_03.gif>. Then, the <img src=image/13492345_05.gif> graph of a group <img src=image/13492345_03.gif>, denoted by <img src=image/13492345_06.gif>, is the simple undirected graph in which two distinct vertices <img src=image/13492345_07.gif> are connected to each other by an edge if and only if both vertices satisfy <img src=image/13492345_08.gif>. The main contribution of this paper is to construct the <img src=image/13492345_05.gif> graph using the elements of Mathieu group, <img src=image/13492345_09.gif>. Additionally, the connectivity of <img src=image/13492345_06.gif> has been proven as a connected graph. Finally, an open problem is highlighted in addressing future research.