Conjugate Graph and Some Properties of the SL(2,3) Group

Conjugate graph is a graph in which the vertices are the non central elements of a group and two vertices are adjacent if they are conjugate. In this paper, the conjugate graph of SL(2,3) is first calculated and then its adjacency matrix, Laplacian, spectrum, line graph and complement graphs are found. We also calculate the different graph properties like clique number, dominating number, chromatic number and independence number of this graph.