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The b-chromatic Number of Some Corona Graphs
LV Chuang, WANG Ke-lun
2018, 35 (4):
445-456.
doi: 10.3969/j.issn.1005-3085.2018.04.007
Let {V1,V2,⋯,Vk} be a proper vertex coloring of a graph G=(V,E), which is called a b-coloring of G, if for all i,j:1≤i≠j≤k, exists u∈Vi,v∈Vj, satisfying uv∈E. The maximum positive integer k for a b-coloring {V1,V2,⋯,Vk} on a graph G is called the b-chromatic number, denoted by b(G). A graph G is called b-continuity if for all k:χ(G)≤k≤b(G), there exists a (k)b-coloring on graph G. According to the structural characteristics of the Corona graphs, the cyclic coloring schemes are constructed. Through the cyclic coloring on two kinds of vertices of Corona graphs, the b-chromatic number of several Corona graphs equalling to its m-degree is obtained, and all these Corona graphs are b-continuous.
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