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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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References

  1. Arumugam, S., Bagga, J., Chandrasekar, K.R.: On dominator colorings in graphs. Proc. Math. Sci. 122(4), 561–571 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chellali, M., Maffray, F.: Dominator colorings in some classes of graphs. Graphs Comb. 28(1), 97–107 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Gera, R., Rasmussen, C., Horton, S.: Dominator colorings and safe clique partitions. Congressus Numerantium 181, 19–23 (2006)

    MathSciNet  MATH  Google Scholar 

  4. Gera, R.: On dominator colorings in graphs. Graph Theory Notes N. Y. LII, 25–30 (2007)

    MathSciNet  Google Scholar 

  5. Gera, R.: On the dominator colorings in bipartite graphs. Inf. Technol. New Gen. ITNG’07, 947–952 (2007)

    Google Scholar 

  6. Jacobson, M.S., Kinch, L.F.: On the domination number of products of graphs I. Ars Combinatoria 18, 33–44 (1984)

    MathSciNet  MATH  Google Scholar 

  7. Merouane, H.B., Chellali, M.: On the dominator colorings in trees. Discussiones Mathematicae Graph Theory 32(4), 677–683 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Nandi, M., Parui, S., Adhikari, A.: The domination numbers of cylindrical grid graphs. Appl. Math. Comput. 217(10), 4879–4889 (2011)

    MathSciNet  MATH  Google Scholar 

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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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