ANALYSING THE COMMUTING GRAPHS FOR ELEMENTS OF ORDER 3 IN MATHIEU GROUPS

Assume that G is a finite group and X is a subset of G. The commuting graph is denoted by С(G,X) which has a set of vertices X with two distinct vertices x, y  X being connected together on the condition of xy = yx. In this paper, computational approaches applied to investigate the structure of commuting graphs Ϲ(G,X) when G is one of the Mathieu groups along with X a G-conjugacy class for elements of order 3. We will pay particular attention to analyze the discs structure and determinate the diameters, girths and the clique number for these graphs.