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- W1925827728 abstract "A graph $G$ is called well-covered if all maximal independent sets of vertices have the same cardinality. A well-covered graph $G$ is called uniformly well-covered if there is a partition of the set of vertices of $G$ such that each maximal independent set of vertices has exactly one vertex in common with each part in the partition. The problem of determining which graphs is well-covered, was proposed in 1970 by M.D. Plummer. Let $cal G$ be the class of graphs with some disjoint maximal cliques covering all vertices. In this paper, some necessary and sufficient conditions are presented to recognize which graphs in the class $cal G$ are well-covered or uniformly well-covered. This characterization has a nice algebraic interpretation according to zero-divisor elements of edge ring of graphs which is illustrated in this paper." @default.
- W1925827728 created "2016-06-24" @default.
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- W1925827728 date "2010-09-27" @default.
- W1925827728 modified "2023-09-27" @default.
- W1925827728 title "Well-covered and uniformly well-covered graphs" @default.
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