The vertex-nullity interlace polynomial of a graph, described by Arratia, BollobÃ¡s and Sorkin in [ABS00] as evolving from questions of DNA sequencing, and extended to a two-variable interlaceâ€¦ (More)

Algebraic techniques are used to find several new combinatorial interpretations for valuations of the Martin polynomial, M(G; s), for unoriented graphs. The Martin polynomial of a graph, introducedâ€¦ (More)

The Martin polynomials, introduced by Martin in his 1977 thesis, encode information abo families of circuits in Eulerian graphs and digraphs. The circuit partition polynomials, J (G;x) and j ( G;x),â€¦ (More)

In this survey, we give a friendly introduction from a graph theory perspective to the q-state Potts model, an important statistical mechanics tool for analyzing complex systems in which nearestâ€¦ (More)

In [BR01], [BR02], BollobÃ¡s and Riordan generalized the classical Tutte polynomial to graphs cellularly embedded in surfaces, i.e. ribbon graphs, thus encoding topological information not captured byâ€¦ (More)

We begin our exploration of graph polynomials and their applications with the Tutte polynomial, a renown tool for analyzing properties of graphs and networks. This two-variable graph polynomial, dueâ€¦ (More)

A graph polynomial is an algebraic object associated with a graph that is usually invariant at least under graph isomorphism. As such, it encodes information about the graph, and enables algebraicâ€¦ (More)