Graph and the Multiplicity of Root 2 in the Chromatic Polynomial

Abstract:

      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.