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International Conference on Theoretical Computer Science and Discrete Mathematics

ICTCSDM 2016: Theoretical Computer Science and Discrete Mathematics pp 144–151Cite as

Dominator Coloring of Generalized Petersen Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10398))

Abstract

A vertex coloring \(\mathcal {C}=\{V_1,V_2,\dots ,V_k\}\) of a graph G is called a dominator coloring of G if every vertex v of G is adjacent to all the vertices of at least one color class \(V_i.\) The dominator chromatic number \(\chi _d(G)\) is the minimum number of colors required for a dominator coloring. In this paper we determine the dominator chromatic number of the generalized Petersen graph P(n, k) where \(1\le k\le 3\).

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Acknowledgments

The first two authors are thankful to the management of Kalasalingam University for providing fellowship.

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Authors and Affiliations

  1. National Centre for Advanced Research in Discrete Mathematics (n-CARDMATH), Kalasalingam University, Anand Nagar, Krishnankoil, 626126, Tamil Nadu, India

    J. Maria Jeyaseeli, Nazanin Movarraei & S. Arumugam

Authors
  1. J. Maria Jeyaseeli
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  2. Nazanin Movarraei
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  3. S. Arumugam
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Corresponding author

Correspondence to J. Maria Jeyaseeli .

Editor information

Editors and Affiliations

  1. Kalasalingam University, Krishnankoil, India

    S. Arumugam

  2. Ball State University, Muncie, Indiana, USA

    Jay Bagga

  3. Indiana University – Purdue University, Fort Wayne, Indiana, USA

    Lowell W. Beineke

  4. Indian Institute of Technology, New Delhi, India

    B.S. Panda

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Jeyaseeli, J.M., Movarraei, N., Arumugam, S. (2017). Dominator Coloring of Generalized Petersen Graphs. In: Arumugam, S., Bagga, J., Beineke, L., Panda, B. (eds) Theoretical Computer Science and Discrete Mathematics. ICTCSDM 2016. Lecture Notes in Computer Science(), vol 10398. Springer, Cham. https://doi.org/10.1007/978-3-319-64419-6_19

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  • DOI: https://doi.org/10.1007/978-3-319-64419-6_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-64418-9

  • Online ISBN: 978-3-319-64419-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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