A Generalization of Favaron’s Theorem

A graph is \({{well \; covered}}\) if every maximal independent set has the same size and \({very \;well\; covered}\) if every maximal independent set contains exactly half the number of vertices. In this paper, we present an alternative characterization of a certain sub-class of well-covered graphs and show that this generalizes a characterization of very well covered graphs given by Favaron [3].