Vadim E. Levit, Eugen Mandrescu
Published 2016-10-13Version 1
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-well-covered 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.
Comments: 16 pages; 4 figures
Very well-covered graphs with log-concave independence polynomials
On graphs having maximal independent sets of exactly $t$ distinct cardinalities
Very well-covered graphs and the unimodality conjecture
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