Corona图Pn°F1,m、Cn°Cm与Cn°F1,m的b-染色数

摘要

在图G=(V,E)的一个正常染色{V1,V2,…,Vk}中,若(A)i,j,1≤i≠j≤k,(E)u∈Vi,v∈Vj,使得uv∈E,称该染色为b-染色.令b(G)=max{k|V1,V2,…,Vk:(A)i,j,1≤i≠j≤k,(E)u∈Vi,v∈Vj,uv∈E}, 称b(G)为图G的b-染色数.一个图G是b-连续的,如果(A)k:X(G)≤k≤b(G),用k种颜色可实现对G进行b-染色.通过构造特殊染色方案,研究了Corona图Pn°F1,m、Cn°Cm与Cn°F1,m的b-染色数与b-连续性.%For a proper coloring {V1,V2,…,Vk} of graph G=(V,E) if(A)i,j,1≤i≠j≤k,(E)u∈Vi,v∈Vj, that making uv∈E, this coloring is called b-coloring.Let b(G)=max{k|V1,V2,… ,Vk:(A)i,j,1≤i≠j≤k,(E)u∈Vi,v∈Vj,uv∈E}, then it will be called b-chromatic number of graph G.A graph G is of b-continuity if and only if (A)k:X(G)≤k≤b(G) and the b-coloring of G can be realized with k colors.By means of constructing a special coloring plan, the b-chromatic number and b-continuity of Corona graph Pn°F1,m,Cn°Cm and Cn°F1,m are studied.