一类5-桥图的色唯一性

The chromatic uniqueness of a family of 5-bridge graphs

P(G ;λ)是图G关于变量λ的色多项式。如果对任意图H ,P(H ;λ) =P(G ;λ) ,都有H和G同构 ,则称图G是色唯一的。由连接两个顶点的s条内部不交的路组成的图叫s 桥图。本文给出了一类 5 桥图F(2 ,2 ,2 ,a ,b) (a b 3)是色唯一的充分必要条件。推广了关于 5 桥图色唯一性的已有结论。

let P(G;λ)denote the chromatic polynomial of a graph G,expressed in the variable λ.Two graph G and H are said to be chromatically equivalent if P(G)=P(H). A graph G is said to be chromatically unique if P(G)=P(H)implies H is isomorphic to G.The graph consisting of s paths joining two vertices is called a s-bridge graph .In this paper,we give the sufficient and necessary conditions for a family of 5-bridge graph to be chromatically unique and generalize certain results about the chromatic uniqueness of 5-bridge graphs which have been obtained.