Displaying similar documents to “Degree polynomial for vertices in a graph and its behavior under graph operations”

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.

Bipartition Polynomials, the Ising Model, and Domination in Graphs

Markus Dod, Tomer Kotek, James Preen, Peter Tittmann (2015)

Discussiones Mathematicae Graph Theory

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This paper introduces a trivariate graph polynomial that is a common generalization of the domination polynomial, the Ising polynomial, the matching polynomial, and the cut polynomial of a graph. This new graph polynomial, called the bipartition polynomial, permits a variety of interesting representations, for instance as a sum ranging over all spanning forests. As a consequence, the bipartition polynomial is a powerful tool for proving properties of other graph polynomials and graph...

The Eccentric Connectivity Polynomial of some Graph Operations

Ashrafi, A., Ghorbani, M., Hossein-Zadeh, M. (2011)

Serdica Journal of Computing

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The eccentric connectivity index of a graph G, ξ^C, was proposed by Sharma, Goswami and Madan. It is defined as ξ^C(G) = ∑ u ∈ V(G) degG(u)εG(u), where degG(u) denotes the degree of the vertex x in G and εG(u) = Max{d(u, x) | x ∈ V (G)}. The eccentric connectivity polynomial is a polynomial version of this topological index. In this paper, exact formulas for the eccentric connectivity polynomial of Cartesian product, symmetric difference, disjunction and join of graphs are presented. ...