Bipartite Powers of Certain Classes of Bipartite Graphs

TL;DR

This paper investigates how bipartite powers affect certain classes of bipartite graphs, showing closure properties for interval bigraphs, proper interval bigraphs, and chordal bipartite graphs under bipartite powers.

Contribution

It establishes that interval bigraphs, proper interval bigraphs, and chordal bipartite graphs are closed or strongly closed under bipartite powers, extending understanding of graph power operations.

Findings

Interval bigraphs are closed under bipartite powers.

Proper interval bigraphs are closed under bipartite powers.

Chordal bipartite graphs are strongly closed under bipartite powers.

Abstract

The concept of graph powers has been extensively studied in graph theory. Analogous to graph powers, Chandran et al. [3] introduced the notion of bipartite powers for bipartite graphs. In this paper, we show that the class of interval bigraphs, as well as the class of proper interval bigraphs are closed under the operation of taking bipartite powers. Finally, we define strongly closed property for bipartite graphs under powers and have shown that the class of chordal bipartite graphs is strongly closed under bipartite powers.