Graph Operations Preserving W2-Property

Vadim E. Levit, Eugen Mandrescu

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)35-40
Number of pages6
JournalElectronic Notes in Discrete Mathematics
StatePublished - Jul 2018


  • class W
  • corona of graphs
  • graph join
  • independent set
  • rooted product of graphs
  • shedding vertex
  • well-covered graph


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