Displaying similar documents to “Bipartition Polynomials, the Ising Model, and Domination in Graphs”

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.

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...