On Powers of Strongly Chordal and Circular Arc Graphs

Abstract

In this paper, we study the powers of two important classes of graphs — strongly chordal graphs and circular arc graphs. We show that for any positive integer $k\ge 2$, $G^{k-1}$ is a strongly chordal graph implies $G^k$ is a strongly chordal graph. In case of circular arc graphs, we show that every integral power of a circular arc graph is a circular arc graph.