Resize result involution graphs of some finite groups

The resize result involution graph of a finite group , is a simple undirected graph whose vertices are the conjugacy classes of and two distinct vertices are adjacent if their representative product is a non-trivial involution. In this paper, we describe an algorithm to obtain the resize result involution graphs. Also, we prove that the resize result involution graphs for , , the Janko groups , the Held group and the exceptional group 2 are connected with diameter at most and girth . We find some properties of the resize result involution graphs. The properties of these graphs are obtained by using GAP and YAGs packages.