The clique operator on graphs with few P4 P 4 's
The clique graph of a graph G  is the intersection graph K(G) K ( G ) of the (maximal) cliques of G . The iterated clique graphs Kn(G) K n ( G ) are defined by K0(G)=G K 0 ( G ) = G and K i ( G ) = K ( K i - 1 ( G ) ) , i > 0 and K is the clique operator. In this article we use the modular decomposition technique to characterize the K -behaviour of some classes of graphs with few P4 P 4 's . These characterizations lead to polynomial time algorithms for deciding the K-convergence or K-divergence of any graph in the class.
iterated clique graphs modular decompositions clique divergence p4 p 4 -tidy graphs p4 p 4 p4 p 4 p 4