In the previous paper, it was shown that the graph U. ÷ 1 obtained from the wheel W n ÷ 1 by deleting a spoke is uniquely determined by its chromatic polynomial if n >i 3 is odd. In this paper, we show that the result is also true for even n >~ 4 except when n = 6 in which case, the graph W given in the paper is the only graph having the same chromatic polynomial as that of U 7. The relevant to...

The Tutte polynomial is a fundamental invariant of graphs. In this article, we define and study a generalization of the Tutte polynomial for directed graphs, that we name B-polynomial. The B-polynomial has three variables, but when specialized to the case of graphs (that is, digraphs where arcs come in pairs with opposite directions), one of the variables becomes redundant and the B-polynomial ...

Motivated by certain conjectures regarding immanants of Jacobi-Trudi matrices, Stanley has recently defined and studied a symmetric function generalization XG of the chromatic polynomial of a graph G. Independently, Chung and Graham have defined and studied a directed graph invariant called the cover polynomial. The cover polynomial is closely related to the chromatic polynomial and to the rook...

By h(G, x) and P (G, λ) we denote the adjoint polynomial and the chromatic polynomial of graph G, respectively. A new invariant of graph G, which is the fourth character R4(G), is given in this paper. Using the properties of the adjoint polynomials, the adjoint equivalence class of graph Bn−6,1,2 is determined, which can be regarded as the continuance of the paper written by Wang et al. [J. Wan...