Very well covered graphs

Abstract

AbstractA graph is well-covered if it has no isolated vertices and all the maximal stable (independent) sets have the same cardinality. If furthermore this cardinality is equal to 12n, where n is the order of the graph, the graph is called ‘very well covered’. The class of very well-covered graphs contains in particular the bipartite well-covered graphs studied by Ravindra. In this article, we characterize the very well covered-graphs and give some of their properties