图U_n∪K_4^-的色等价刻画

A characterization for chromatic equivalence of graph U_n∪K_4^-

h(G,x)表示图G的伴随多项式,它从图G的补图出发研究色惟一和色等价.若P(G,λ)=P(H,λ),称G和H色等价.一个图被称为是色惟一的,如P(G,λ)=P(H,λ)意味着GH.若h(G,x)=h(H,x),称G和H伴随等价;G和H色等价当且仅当G和H伴随等价;G色惟一当且仅当G伴随惟一.Un表示从路Pn-4的每个1度点分别引出两个悬挂边所得到的具有两个3度点4个1度点的树.K-4表示从K4中删去一条边得到的图.应用伴随多项式理论研究了图Un∪K-4的伴随多项式系数和根的性质,以此为基础刻画了图Un∪K-4的色等价图类.

Let h（ G, x） denote the adjoint polynomial of a Graph G. The chromatic uniqueness and chomatic equivalence from the complement of Graph G are studied, ff P（ G, λ ） = P（ H, λ ）, G and H are called chromatic equivalence. A graph is called chromatic uniqueness, if P（ G,λ ） = P（ H, λ ）, then G≈ H. ff h（ G, x） = h（ H, x）, then G and H are adjoint equivalent; G and H is chromatically equivalent if and only if G and H^- are adjoint equivalent; G is chromatic unique if and only if G^- is adjoint unique. Un is a tree with two vertices of degree 3 and four vertices of degree 1 obtained from path Pn-4 by adding two hanging edges of every vertex of degree 1. K4^- is a graph in which an edge is removed from K4 . The coefficient of adjoint polynomial and the property of its root about graph （UnUK4^-）^- are discussed on the basis of the theory of adjoint polynomial, and its chromatically equivalent classes are characterized.