When G^2 is a Konig-Egervary graph?

TL;DR

This paper characterizes when the square of a graph is a Konig-Egervary graph, establishing that this occurs precisely when the original graph is both square-stable and Konig-Egervary.

Contribution

It provides a necessary and sufficient condition linking the properties of G and its square G^2 regarding Konig-Egervary graphs and square-stability.

Findings

G^2 is Konig-Egervary iff G is square-stable and Konig-Egervary

Characterizes the structure of graphs with Konig-Egervary squares

Establishes a clear equivalence condition for G^2 to be Konig-Egervary

Abstract

The square of a graph G is the graph G^2 with the same vertex set as in G, and an edge of G^2 is joining two distinct vertices, whenever the distance between them in G is at most 2. G is a square-stable graph if it enjoys the property alpha(G)=alpha(G^2), where alpha(G) is the size of a maximum stable set in G. In this paper we show that G^2 is a Konig-Egervary graph if and only if G is a square-stable Konig-Egervary graph.