On clique convergence of graphs

Let G be a graph and KG be the set of all cliques of G, then the clique graph of G denoted by K(G) is the graph with vertex set KG and two elements Qi,Qj∈KG form an edge if and only if Qi∩Qj≠0̸. Iterated clique graphs are defined by K0(G)=G, and Kn(G)=K(Kn−1(G)) for n>0. In this paper we prove a necessary and sufficient condition for a clique graph K(G) to be complete when G=G1+G2, give a partial characterization for clique divergence of the join of graphs and prove that if G1, G2 are Clique-Helly graphs different from K1 and G=G1□G2, then K2(G)=G.