DIAMETERS OF ITERATED CLIQUE GRAPHS OF CHORDAL GRAPHS

The clique graph K(G) of a graph is the intersection graph of maximal cliques of G. The iterated clique graph Kn(G) is inductively defined as K(Kn−1(G)) and K1(G) = K(G). Let the diameter diam(G) be the greatest distance between all pairs of vertices of G. We show that diam(Kn(G)) = diam(G) — n if G is a connected chordal graph and n ≤ diam(G). This generalizes a similar result for time graphs by Bruce Hedman. Copyright © 1990 Wiley Periodicals, Inc., A Wiley Company