A hierarchy of self-clique graphs
نویسندگان
چکیده
The clique graph K(G) of G is the intersection graph of all its (maximal) cliques. A connected graph G is self-clique whenever G ∼= K(G). Self-clique graphs have been studied in several papers. Here we propose a hierarchy of self-clique graphs: Type 3 ( Type 2 ( Type 1 ( Type 0. We give characterizations for classes of Types 3, 2 and 1 (including Helly self-clique graphs) and several new constructions of families of self-clique graphs. It is shown that all (but one) previously published examples of self-clique graphs are of Type 2. Our methods provide a uni?ed approach and generalizations of those examples. As further applications, we give a characterization of the self-clique graphs such that at most 3 cliques have more than two vertices (they are all of Type 2) and a description of the diamond-free graphs of Type 2. c © 2004 Elsevier B.V. All rights reserved.
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عنوان ژورنال:
- Discrete Mathematics
دوره 282 شماره
صفحات -
تاریخ انتشار 2004