On Clique Convergences of Graphs
نویسندگان
چکیده
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 6= ∅. Iterated clique graphs are defined by K0(G) = G, and K(G) = K(Kn−1(G)) for n > 0. In this paper we determine the number of cliques in K(G) when G = G1+G2, prove a necessary and sufficient condition for a clique graph K(G) to be complete when G = G1+G2, give a characterization for clique convergence of the join of graphs and if G1, G2 are Clique-Helly graphs different from K1 and G = G1 G2, then K2(G) = G.
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