一类色等价图的图特征

Characteristics of a Class Chromatic Equivalence Graphs

给出了一个有割点的连通图Ｇ是色唯一的充分必要条件为Ｇ由一个色唯一、顶点可迁图连一尾构成．进而证明了若Ｍ为色唯一，不含分离边的连通图，且Ｐ（Ｇ，λ）＝（λ－１）Ｋｐ（Ｍ），则Ｇ含一子图同构于Ｍ及Ｋ个桥．

Following results are given:First, let G be a connected graph with cutpoint,then G is chromatiically unique if and only if G is a chromatcally unique, vertex transitive graph with a tail. Then on the base of above result, it is proved that if P(G)=(λ-1) kP(M) , where M is a chromatically unique connected graph without separating edge, then G contains a subgraph isomorphic to M and K bridges.