On α-Square-Stable Graphs
نویسنده
چکیده
The stability number of a graph G, denoted by α(G), is the cardinality of a maximum stable set, and μ(G) is the cardinality of a maximum matching in G. If α(G) + μ(G) equals its order, then G is a König-Egerváry graph. We call G an α-square-stable graph if α(G) = α(G), where G denotes the second power of G. These graphs were first investigated by Randerath and Wolkmann, [18]. In this paper we obtain several new characterizations of α-square-stable graphs. We also show that G is an α-square-stable König-Egerváry graph if and only if it has a perfect matching consisting of pendant edges. Moreover, we find that well-covered trees are exactly α-square-stable trees. To verify this result we give a new proof of one Ravindra’s theorem describing well-covered trees, [19].
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