Displaying similar documents to “Mean value for the matching and dominating polynomial”

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...

Degree polynomial for vertices in a graph and its behavior under graph operations

Reza Jafarpour-Golzari (2022)

Commentationes Mathematicae Universitatis Carolinae

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We introduce a new concept namely the degree polynomial for the vertices of a simple graph. This notion leads to a concept, namely, the degree polynomial sequence which is stronger than the concept of degree sequence. After obtaining the degree polynomial sequence for some well-known graphs, we prove a theorem which gives a necessary condition for the realizability of a sequence of polynomials with positive integer coefficients. Also we calculate the degree polynomial for the vertices...