منابع مشابه
B-coloring of Cartesian Product of Trees
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 a neighbor in each of the other color classes. The largest positive integer k for which G has a b-coloring using k colors is the b-chromatic number b(G) of G. The b-spectrum Sb(G) of a graph G is the set of positive integers k...
متن کاملOn b-coloring of cartesian product of graphs
A b-coloring of a graph G by k colors is a proper k-coloring of the vertices of G such that in each color class there exists a vertex having neighbors in all the other k−1 color classes. The b-chromatic number φ(G) of a graph G is the maximum k for which G has a b-coloring by k colors. This concept was introduced by R.W. Irving and D.F. Manlove in 1999. In this paper we study the b-chromatic nu...
متن کاملb-coloring in Square of Cartesian Product of Two Cycles
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...
متن کاملOn the b-coloring of cartesian product of graphs
A b-coloring of a graph G by k colors is a proper k-coloring of the vertices of G such that in each color class there exists a vertex having neighbors in all the other k − 1 color classes. The b-chromatic number φ(G) of a graph G is the maximum k for which G has a b-coloring by k colors. This concept was introduced by R.W. Irving and D.F. Manlove in 1999. In this paper we study the b-chromatic ...
متن کاملGame coloring the Cartesian product of graphs
This article proves the following result: Let G and G′ be graphs of orders n and n′, respectively. Let G∗ be obtained from G by adding to each vertex a set of n′ degree 1 neighbors. If G∗ has game coloring number m and G′ has acyclic chromatic number k, then the Cartesian product G G′ has game chromatic number at most k(k+m − 1). As a consequence, the Cartesian product of two forests has game c...
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ژورنال
عنوان ژورنال: Taiwanese Journal of Mathematics
سال: 2016
ISSN: 1027-5487
DOI: 10.11650/tjm.20.2016.5062