【摘要】：在一個圖G的正常k染色中,如果每一個顏色類中都至少存在一個頂點,使得其在其它的k-1個顏色類中都至少有一個鄰居,則稱這樣的正常k染色為b-染色.一個圖G的b-染色數(shù)是最大的正整數(shù)k,使得用k種顏色能夠對G進行b-染色,用b(G)來表示.如果對于任意的正整數(shù)k:χ(G)≤k≤b(G),用k種顏色可以對圖G進行b-染色,則稱圖G是b-連續(xù)的.設G1與G2為任意圖,稱圖G=G_1·G_2為圖G_1與G_2的Corona圖,其中G包含G_1的一個拷貝,包含G_2的|V(G_1)|個拷貝,且G_1的第i個頂點與G_2的第i個拷貝的所有頂點都鄰接.研究了路圖與路圖、星形圖以及輪圖所構成的Corona圖P_n·P_m、P_n·K_(1,m)以及P_n·W_(m+1)的m-度,b-染色數(shù)與b-連續(xù)性.
[Abstract]:In the normal k-coloring of a graph G, if there is at least one vertex in each color class such that it has at least one neighbor among the other k-1 color classes, then such normal k-coloring is called b-coloring. The b-coloring number of a graph G is the largest positive integer k, so that the k-color can be used to b-coloring G, which is represented by b (G). If for any positive integer k: 蠂 (G) 鈮，

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