Edge Clique Graphs of Some Important Classes of Graphs

Abstract

In this paper we study the edge clique graph $K(G)$ of many classes of intersection graphs $G$ — such as graphs of boxicity $\le k$, chordal graphs and line graphs. We show that in each of these cases, the edge clique graph $K(G)$ belongs to the same class as $G$. Also, we show that if $G$ is a $W_4$-free transitivity orientable graph, then $K(G)$ is a weakly $\theta$-perfect graph.