图和色多项式根2的阶

Graph and the Multiplicity of Root 2 in the Chromatic Polynomial

中文关键词:  色多项式  块  可分块  非偶可分块.

英文关键词:chromatic polynomial  block  separable block  non-even separable block.

中文摘要:

      本文证明了3-连通非偶图的色多项式根2的阶为1;满足一定条件的非3-连通非偶图的色多项式根2的阶是图的非偶块和非偶可分块数.从而，把色多项式P(G)中1的阶是图G的非平凡块数这一结果进一步加以推广.

英文摘要:

      In this paper, it was proved that the multiplicity of the root 2 in the chromatic polynomial of 3-connected non-even graph is 1; and it is showed that the multiplicity of the root 2 in the chromatic polynomial of non-3-connected graph with definite conditions is equal to the number of non-even blocks and non-even separable blocks. Therefore, it was spreaded that the multiplicity of the root 1 in the chromatic polynomial of a simple graph G is equal to the numble of nontrivial blocks in G.