Clique Graphs of Chordal and Path Graphs
Jayme Luiz SZWARCFITER, Claudson Ferreira Bornstein · SIAM Journal on Discrete Mathematics · 1994
Clique graphs of chordal and path graphs are characterized. A special class of graphs named expanded trees is discussed. It consists of a subclass of disk-Helly graphs. It is shown that the clique graph of every chordal (hence path) graph is an expanded tree. In addition, every expanded tree is the clique graph of some path (hence chordal) graph. Different characterizations of expanded trees are described, leading to a polynomial time algorithm for recognizing them.