图P_n~k的着色

设k是一个正整数,在含有n个顶点的路Pn=v1v2…vn上,当且仅当两点的距离为k(k≥2)时增加一条边,这样所得到的图叫做Pnk(v1,vn),有时Pkn(v1,vn)也简记为Pnk.论文研究图Pnk的点着色、边着色和点、边全着色,得到图Pnk的点色数、边色数和图Pnk满足点、边全着色猜想等结论.

The colouring of graph P_n~k

As k is integer,in a rote Pn=v1v2…vn of n vertex,the graph was called P_n~k(v1,vn),if and only if the distance of two vertex was k(k≥2),there was a edge in the two vertex.The vertex colouring、edge colouring and vertex-edge total colouring of graph P_n~k were studied in the paper.We obtained the vertex chromatic number and edge chromatic number of the graph P_n~k,and the total colouring conjecture was ture at the graph P_n~k,etc.