Powers of hhd-free graphs∗
Feodor F. Dragan, Falk Nicolai, Andreas Brandstädt · International Journal of Computer Mathematics · 1998
The k-the power of a graph G is the graph with the same vertex set as G where two vertices are adjacent iff their distance in G is at most k. In this paper we consider HHD-free graphs, i.e., the graphs where each cycle of length at least five has two chords. We show, that odd powers of HHD-free graphs are again HHD-free, and characterize those HHD-free graphs by forbidden subgraphs for which odd powers are chordal, and even powers are HHD-free or chordal, respectively.