关于色唯一图的注记

A note on chromatic uniqueness of graphs

设P(G;λ)是图G的色多项式,如果对任意图H,当P(H;λ)=P(G;λ)时,都有H和G同构,则称图G是色唯一的。本文给出了由两个块H和K2构成的图G是色唯一的当且仅当H是色唯一点可迁的。

let P( G ;λ) denote the chromatic polynoical of a graph G. A graph G is said to be chromatically unique if P(H;λ) = P(G;λ) implies H is isomorphic to G. In this paper, we proved that if the two blocks of a connected graph G are H and K2, then G is chromatically unique if and only if H is vertex-transitive and chromatically unique.