Clique divergent graphs with unbounded sequence of diameters
Discrete Mathematics
Locally C6 graphs are clique divergent
Discrete Mathematics
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
The icosahedron is clique divergent
Discrete Mathematics
Clique divergent clockwork graphs and partial orders
Discrete Applied Mathematics - Brazilian symposium on graphs, algorithms and combinatorics
The clique operator on graphs with few P4's
Discrete Applied Mathematics
A new family of expansive graphs
Discrete Applied Mathematics
The clique operator on graphs with few P4's
Discrete Applied Mathematics
Edge contraction and edge removal on iterated clique graphs
Discrete Applied Mathematics
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We study the dynamical behaviour of simple graphs under the iterated application of the clique graph operator k, which transforms each finite graph G into the intersection graph kG of its (maximal) cliques. The graph G is said to be clique divergent if the sequence of the orders o(knG) of the iterated clique graphs of G tends to infinity with n, and G is said to have linear growth if this divergent sequence is bounded by a linear function of n. In this work, we introduce an important family of graphs (the clockwork graphs) which is closed under the clique operator and contains clique divergent graphs with strictly linear growth, i.e., o(knG) = o(G) + rn, where r is any fixed positive integer. We apply our results to give examples of clique divergent graphs having non-strict linear growth.