On the Cartesian product of non well-covered graphs
  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. 
Bert L. Hartnell and Douglas F. Rall
math.CO cs.DM