Proceedings of the International Conference on Theory and Application of Mathematics and Informatics ICTAMI 2005 - Alba Iulia , Romania SQUARE - STABLE AND WELL - COVERED GRAPHS
نویسندگان
چکیده
The stability number of the graph G, denoted by α(G), is the cardinality of a maximum stable set of G. In this paper we characterize the square-stable graphs, i.e., the graphs enjoying the property α(G) = α(G), where G is the graph with the same vertex set as in G, and an edge of G is joining two distinct vertices, whenever the distance between them in G is at most 2. We show that every square-stable graph is well-covered, and wellcovered trees are exactly the square-stable trees.
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