Polynomial invariants of graphs with state models

Polynomial Invariants of Graphs

We define two polynomials f(G) and /*(G) for a graph G by a recursive formula with respect to deformation of graphs. Analyzing their various properties, we shall discuss when two graphs have the same polynomials. Introduction. Our graphs are finite, undirected ones with or without self-loops and multiple edges. As elementary deformations of graphs, we have the deletion and the contraction of ed...

Polynomial invariants of graphs II

Negami and Kawagoe has already defined a polynomial f(G) associated with each graph G as what discriminates graphs more finely than the polynomial f(G) definedby Negami and the Tutte polynomial. In this paper, we shall show that the polynomial f(G) includes potentially the generating function counting the independent sets and the degree sequence of a graph G, which cannot be recognized from f(G...

Graphs determined by polynomial invariants

Many polynomials have been de'ned associated to graphs, like the characteristic, matchings, chromatic and Tutte polynomials. Besides their intrinsic interest, they encode useful combinatorial information about the given graph. It is natural then to ask to what extent any of these polynomials determines a graph and, in particular, whether one can 'nd graphs that can be uniquely determined by a g...

Homomorphisms and Polynomial Invariants of Graphs

This paper initiates a study of the connection between graph homomorphisms and the Tutte polynomial. This connection enables us to extend the study to other important polynomial invariants associated with graphs, and closely related to the Tutte polynomial. We then obtain applications of these relationships in several areas, including Abelian Groups and Statistical Physics. A new type of unique...

Polynomial Invariants of Embeddings of Graphs on Closed Surfaces