Dominator Colorings of Certain Cartesian Products of Paths and Cycles

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• 作者：Qin Chen ; Chengye Zhao ; Min Zhao
• 关键词：Dominator coloring ; Dominator chromatic number ; Cartesian product
• 刊名：Graphs and Combinatorics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：33
• 期：1
• 页码：73-83
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Combinatorics; Engineering Design;
• 出版者：Springer Japan
• ISSN：1435-5914
• 卷排序：33

文摘

A dominator coloring of a graph G is a proper coloring of G with the additional property that every vertex dominates an entire color class. The dominator chromatic number \(\chi _d(G)\) of G is the minimum number of colors among all dominator colorings of G. In this paper, we determine the dominator chromatic numbers of Cartesian product graphs \(P_2 \square P_n\) and \(P_2 \square C_n\).