B - Continuity in Peterson graph and power of a Cycle
نویسندگان
چکیده
A graph G is k-colorable if G has a proper vertex coloring with k colors. The chromatic number (G) is the minimum number k such that G is k-colorable. A bcoloring of a graph with k colors is a proper coloring in which each color class contains a color dominating vertex. The largest positive integer k for which G has a b-coloring with k colors is the b-chromatic number of G, denoted by b(G). The b-spectrum Sb(G) of G, is defined as the set of all integers k at which G is b-colorable with k colors. A graph G is b-continuous if its b-spectrum equals [(G), b(G)]. In this paper, we prove that the Peterson graph and the power of a cycle are b-continuous. Also, we prove that the Cartesian product of two cycles CmCn is b-continuous when m and n are multiples of 5. In this case, we give the color classes of b-coloring with k colors for each k with (G) k b(G).
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