1-well-covered Graphs Revisited

A graph is well-covered if all its maximal independent sets are of the same size (M. D. Plummer, 1970). A well-covered graph (with at least two vertices) is 1-wellcovered if the deletion of every vertex leaves a graph which is well-covered as well (J. W. Staples, 1975). In this paper, we provide new characterizations of 1-well-covered graphs, which we further use to build 1-well-covered graphs by corona, join, and concatenation operations.