%0 Journal Article
%T On Konig-Egervary Square-Stable Graphs
%A Vadim E. Levit
%A Eugen Mandrescu
%J Computer Science
%D 2009
%I arXiv
%X The stability number of a graph G, denoted by alpha(G), is the cardinality of a maximum stable set, and mu(G) is the cardinality of a maximum matching in G. If alpha(G)+mu(G) equals its order, then G is a Konig-Egervary graph. In this paper we deal with square-stable graphs, i.e., the graphs G enjoying the equality alpha(G)=alpha(G^{2}), where G^{2} denotes the second power of G. In particular, we show that a Konig-Egervary graph is square-stable if and only if it has a perfect matching consisting of pendant edges, and in consequence, we deduce that well-covered trees are exactly the square-stable trees.
%U http://arxiv.org/abs/0908.1313v3