The Entire Sub-map. On The Second Q-tree And Three Of The Whole Child Chromaticity Of The Study

The graphs we argued here are simple and undirected ones .In this paper ,we proved that:Theorem 1If the minimum degree of a graph G does not equal q -3, then the graphs which have the chromatic polynomial as following P (G ;λ)=λ(λ-1)(λ-q+2)(λ-q+1)³ (λ-q)^n-q-2 ( n≥q+2) could only be the two-degree integral subgraph of q -tree ,or the added-vertex q -tree on n vertices.Theorem 2(1)We assume that the chromatic polynomial of three-degree integral subgraph G of q -tree on n vertices is P (G ;λ)=λ(λ-1)(λ-q+2)(λ-q+1)⁴ (λ-q)^n-q-3( n≥q+3), then G is a (q +1) colorable graph ,its number of color partitions is eight.(2)On the contrary , if under a ( q +1) colored, just exists one disconnected two color subgraph ,then G which has the chromatic polynomial like above is a three-degree integral subgraph of q -tree on n vertices.