Abstract
A graph is well-covered if all its maximal independent sets are of the same size (Plummer, 1970). A graph G belongs to class Wn if every n pairwise disjoint independent sets in G are included in n pairwise disjoint maximum independent sets (Staples, 1975). Clearly, W1 is the family of all well-covered graphs. Staples showed a number of ways to build graphs in Wn, using graphs from Wn or Wn+1. In this paper, we construct some more infinite subfamilies of the class W2 by means of corona, join, and rooted product of graphs.
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