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Equitable distinguishing chromatic number

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Abstract

We introduce the equitable distinguishing chromatic number \(\chi _{ED}(G)\) of a graph G as the least number k such that G has an equitable coloring with k colors that is only preserved by the trivial automorphism. The equitable distinguishing chromatic number of some graphs such as paths, cycles, trees, and Cartesian products of two complete graphs are determined.

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Acknowledgements

The authors are deeply grateful to the referee for careful reading of the manuscript and helpful suggestions. Also they are deeply grateful to Professors R. Kalinowski and M. Pilśniak for participant in a workshop in Ferdowsi University of Mashhad in 2018. This work has been done during the first author’s visit to the Department of Mathematics, Ferdowsi University of Mashhad in 2018. She wishes to thank the department for warm hospitality.

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Authors and Affiliations

  1. Department of Mathematics, Quchan University of Technology, P.O.Box 94771-67335, Quchan, Iran

    Tayyebeh Amouzegar

  2. Department of Pure Mathematics, Faculty of Mathematical Sciences and Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P. O. Box 1159-91775, Mashhad, Iran

    Kazem Khashyarmanesh

Authors
  1. Tayyebeh Amouzegar
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  2. Kazem Khashyarmanesh
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Correspondence to Kazem Khashyarmanesh.

Additional information

Communicated by Sharad S Sane, PhD.

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Amouzegar, T., Khashyarmanesh, K. Equitable distinguishing chromatic number. Indian J Pure Appl Math 53, 304–315 (2022). https://doi.org/10.1007/s13226-021-00004-z

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