b-coloring in Square of Cartesian Product of Two Cycles
نویسنده
چکیده
A b-coloring of a graph G with k colors is a proper coloring of G using k colors in which each color class contains a color dominating vertex, that is, a vertex which has at least one neighbor in each of the other color classes. The largest integer k(>0) for which G has a b-coloring using k colors is the b-chromatic number b(G) of G. In this paper, we obtain the b-chromatic number of the square of Cartesian product of two cycles. Further, we obtained the b-coloring number of Cn K2 and Cn K3 and prove that these graphs are b-continuous for some particular values of n. AMS Mathematics Subject Classification (2010): 05C15
منابع مشابه
Coloring the square of the Cartesian product of two cycles
The square G2 of a graph G is defined on the vertex set of G in such a way that distinct vertices with distance at most two in G are joined by an edge. We study the chromatic number of the square of the Cartesian product Cm2Cn of two cycles and show that the value of this parameter is at most 7 except when m = n = 3, in which case the value is 9, and when m = n = 4 or m = 3 and n = 5, in which ...
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