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Dominator Colorings of Certain Cartesian Products of Paths and Cycles

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Abstract

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 \(P_2 \square C_n\).

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Authors and Affiliations

  1. College of Science, China Jiliang University, Hangzhou, 310018, China

    Qin Chen, Chengye Zhao & Min Zhao

Authors
  1. Qin Chen
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  2. Chengye Zhao
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  3. Min Zhao
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Corresponding author

Correspondence to Qin Chen.

Additional information

This research was supported partially by NSFC No. 61173002 and ZJNSF No. LQ14A010014.

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Chen, Q., Zhao, C. & Zhao, M. Dominator Colorings of Certain Cartesian Products of Paths and Cycles. Graphs and Combinatorics 33, 73–83 (2017). https://doi.org/10.1007/s00373-016-1742-7

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  • DOI: https://doi.org/10.1007/s00373-016-1742-7

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