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Coloring the Square of Sierpiński Graphs

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Abstract

The square \(G^2\) of a graph \(G\) is defined on the vertex set \(V(G)\) of \(G\) such that any two vertices with distance at most two in \(G\) are linked by an edge. In this paper, the chromatic number and equitable chromatic number of the square \(S^2(n,k)\) of Sierpiński graph \(S(n,k)\) are studied. It is obtained that \(\chi (S^2(n,k))=\chi _{=}(S^2(n,k))=k+1\) for \(n\ge 2\) and \(k\ge 2\).

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Acknowledgments

The authors would like to thank referees for their helpful suggestions for the improvement of the manuscript. This work is supported by research grants NSFC with codes 61070095, 60873207, and NSFC for youth with code 61103073.

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Authors and Affiliations

  1. School of Science, Linyi University, Linyi, 276005, Shandong, China

    Bing Xue

  2. College of Mathematical Science, Tianjin Normal University, Tianjin, 300387, China

    Liancui Zuo

  3. Department of Mathematics, Shandong University, Jinan, 250100, China

    Guojun Li

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  1. Bing Xue
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  2. Liancui Zuo
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  3. Guojun Li
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Correspondence to Liancui Zuo.

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Xue, B., Zuo, L. & Li, G. Coloring the Square of Sierpiński Graphs. Graphs and Combinatorics 31, 1795–1805 (2015). https://doi.org/10.1007/s00373-014-1444-y

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  • DOI: https://doi.org/10.1007/s00373-014-1444-y

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