Chromatic Equivalent Graphs Of Some Kinds Of Graphs

The notinon of chromatically unique graphs was first introduced and studied by Chao and Whitehead [2]. The main tools of study is chromatic polynomials of graphs. By P(G,λ)denotes chromatic polynomials of G, if P(G,λ) = P(H,λ), then we call Gand H are chromatic equivalent, denoted by G - H; A graph G is called chromatc unique if G≌H, whenever G - H. The related contents can refer to [2,7].In 1987,Professor Ruying Liu first introduced the notion of adjoint polynomials [1,17], which was a method to study chromaticity of graphs by study the complement of their.Denoted by h(G,x) the adjoint polynomials of G, if h(G,x) = h(H,x), we call G and H are adjoint equivalent, denoted by G -_h H; A graph G is called adjoint unique if G≌H, whenever G -_h H. The relation of it and chromatic polynomials are that: G and H are adjoint equivalentif and only if their complement (?) and (?) are chromatic equivalent, and G is adjoint unique if and only if (?) is chromatic unique. The related contents can refer to [9,10,11,15].In this paper, I mainly by use of the properties of adjoint polynomials, such as: divisibility,characters and minimum real roots and so on. Charactered the adjoint equivalent graphs of some graphs, then obtained the chromatic equivalent graphs and the condition of chromatic uniqueness of their complements. The main contents of each chapter of this thesis are as follows:Chapter 1: The preliminary knowledge of adjoint polynomials is introduced;Chapter 2: The chromatic equivalent graphs of (?),(?) are charactered;Chapter 3: The chromatic equivalent graphs of (?)(?)are obtained;Chapter 4: The chromatic uniqueness of (?) are proofed under certain conditions.