On the Cartesian Product of Non Well-Covered Graphs

Bert L Hartnell, Douglas F Rall

Abstract


A graph is well-covered if every maximal independent set has the same cardinality, namely the vertex independence number.  We answer a question of Topp and Volkmann and prove that if the Cartesian product of two graphs is well-covered, then at least one of them must be well-covered.

Keywords


maximal independent set; well-covered; Cartesian product

Full Text: PDF