The Clique Operator, Set Families, and Their Properties

The clique graph of a graph G (denoted by K(G)) is the intersection graph of the maximal cliques of G. In this paper we propose a novel way of looking at problems related to clique graphs by using set families and operators. Many known results in the area can be rewritten in this new language. In addition, this approach permits the identification of the relevant properties of the graphs and families that make the theorems work, allowing in some cases immediate generalization. To exemplify, we show how a recent polynomial time recognition result for a class of clique graphs can be rewritten and applied to other related classes. nowledge the financial support from FAPESP, CNPq, and FOMEC.