Polynomial invariants of graphs II

Negami and Kawagoe has already defined a polynomial f̃(G) associated with each graph G as what discriminates graphs more finely than the polynomial f(G) defined by Negami and the Tutte polynomial. In this paper, we shall show that the polynomial f̃(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) in general, and discuss on f̃(T) of trees T with observations by computer experiments.