Graphs satisfying inequality theta(G(2)) <= theta(G)

Abstract

In this paper. we study the edge clique cover number of squares of graphs, More specifically, we study the inequality theta(G(2)) less than or equal to theta(G) where theta(G) is the edge clique cover number of a graph G. We show that any graph G with at most theta(G) vertices satisfies the inequality. Among the graphs with more than theta(G) vertices, we find some graphs violating the inequality and show that dually chordal graphs and power-chordal graphs satisfy the inequality. Especially, we give an exact formula computing theta(T-2) for a tree T. (C) 2002 Elsevier Science B.V. All rights reserved.