On Unimodality of Independence Polynomials of Some Well-Covered Trees
نویسندگان
چکیده
The stability number α(G) of the graph G is the size of a maximum stable set of G. If sk denotes the number of stable sets of cardinality k in graph G, then I(G;x) = α(G)
منابع مشابه
A Family of Well-Covered Graphs with Unimodal Independence Polynomials
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...
متن کاملOn the unimodality of independence polynomials of very well-covered graphs
The independence polynomial i(G, x) of a graph G is the generating function of the numbers of independent sets of each size. A graph of order n is very well-covered if every maximal independent set has size n/2. Levit and Mandrescu conjectured that the independence polynomial of every very well-covered graph is unimodal (that is, the sequence of coefficients is nondecreasing, then nonincreasing...
متن کاملThe unimodality of independence polynomials of some graphs
In this paper we study unimodality problems for the independence polynomial of a graph, including unimodality, log-concavity and reality of zeros. We establish recurrence relations and give factorizations of independence polynomials for certain classes of graphs. As applications we settle some unimodality conjectures and problems. © 2010 Elsevier Ltd. All rights reserved.
متن کاملIndependence polynomials of well-covered graphs: Generic counterexamples for the unimodality conjecture
A graph G is well-covered if all its maximal stable sets have the same size, denoted by α(G) (M. D. Plummer, 1970). If sk denotes the number of stable sets of cardinality k in graph G, and α(G) is the size of a maximum stable set, then I(G;x) = α(G) ∑ k=0 skx k is the independence polynomial of G (I. Gutman and F. Harary, 1983). J. I. Brown, K. Dilcher and R. J. Nowakowski (2000) conjectured th...
متن کاملUnimodality of the independence polynomials of non-regular caterpillars
The independence polynomial I(G, x) of a graph G is the polynomial in variable x in which the coefficient an on x n gives the number of independent subsets S ⊆ V (G) of vertices of G such that |S| = n. I(G, x) is unimodal if there is an index μ such that a0 ≤ a1 ≤ · · · ≤ aμ−1 ≤ aμ ≥ aμ+1 ≥ · · · ≥ ad−1 ≥ ad. While the independence polynomials of many families of graphs with highly regular stru...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003