Displaying similar documents to “A new two-variable generalization of the chromatic polynomial.”

Mean value for the matching and dominating polynomial

Jorge Luis Arocha, Bernardo Llano (2000)

Discussiones Mathematicae Graph Theory

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The mean value of the matching polynomial is computed in the family of all labeled graphs with n vertices. We introduce the dominating polynomial of a graph whose coefficients enumerate the dominating sets for a graph and study some properties of the polynomial. The mean value of this polynomial is determined in a certain special family of bipartite digraphs.

On the rooted Tutte polynomial

F. Y. Wu, C. King, W. T. Lu (1999)

Annales de l'institut Fourier

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The Tutte polynomial is a generalization of the chromatic polynomial of graph colorings. Here we present an extension called the rooted Tutte polynomial, which is defined on a graph where one or more vertices are colored with prescribed colors. We establish a number of results pertaining to the rooted Tutte polynomial, including a duality relation in the case that all roots reside around a single face of a planar graph.

Restricted partitions.

Jakimczuk, Rafael (2004)

International Journal of Mathematics and Mathematical Sciences

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Combinatorial Nullstellensatz approach to polynomial expansion

Fedor Petrov (2014)

Acta Arithmetica

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Applying techniques similar to Combinatorial Nullstellensatz we prove a lower estimate of |f(A,B)| for finite subsets A, B of a field, and a polynomial f(x,y) of the form f(x,y) = g(x) + yh(x), where the degree of g is greater than that of h.