Powers of Chordal Graphs

Abstract

An undirected simple graph G is called chordal if every circle of G of length greater than 3 has a chord. For a chordal graph G, we prove the following: (i) If m is an odd positive integer, Gm is chordal, (ii) If m is an even positive integer and if Gmis not chordal, then none of the edges of any chordless cycle of Gmis an edge of Gr, rm. © 1983, Australian Mathematical Society. All rights reserved.