Independence Complexes of Well-Covered Circulant Graphs
نویسندگان
چکیده
منابع مشابه
Well-covered circulant graphs
A graph is well-covered if every independent set can be extended to a maximum independent set. We show that it is co-NP-complete to determine whether an arbitrary graph is well-covered, even when restricted to the family of circulant graphs. Despite the intractability of characterizing the complete set of well-covered circulant graphs, we apply the theory of independence polynomials to show tha...
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Let G be a well covered graph, that is, all maximal independent sets of G have the same cardinality, and let ik denote the number of independent sets of cardinality k in G. We investigate the roots of the independence polynomial i(G, x)= ∑ ik xk . In particular, we show that if G is a well covered graph with independence number β, then all the roots of i(G, x) lie in in the disk |z| ≤β (this is...
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T. S. Michael and N. Traves (2002) provided examples of wellcovered graphs whose independence polynomials are not unimodal. A. Finbow, B. Hartnell and R. J. Nowakowski (1993) proved that under certain conditions, any well-covered graph equals G∗ for some G, where G∗ is the graph obtained from G by appending a single pendant edge to each vertex of G. Y. Alavi, P. J. Malde, A. J. Schwenk and P. E...
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If sk equals the number of stable sets of cardinality k in the graph G, then I(G; x) = α(G) ∑ k=0 skx k is the independence polynomial of G (Gutman and Harary, 1983). Alavi, Malde, Schwenk and Erdös (1987) conjectured that I(G; x) is unimodal whenever G is a forest, while Brown, Dilcher and Nowakowski (2000) conjectured that I(G; x) is unimodal for any well-covered graph G. Michael and Traves (...
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We give an alternative characterization for well-covered graphs and restrict this to a characterization for very well covered graphs. We state the conditions under which the intersection of a pair of maximal independent sets of a well-covered graph is maximal and use this result to deene and characterize two recursively decomposable sub-classes of well-covered graphs, one properly containing th...
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ژورنال
عنوان ژورنال: Experimental Mathematics
سال: 2016
ISSN: 1058-6458,1944-950X
DOI: 10.1080/10586458.2015.1091753