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Dominated and dominator colorings over (edge) corona and hierarchical products

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  • Klavžar, Sandi
  • Tavakoli, Mostafa

Abstract

Dominator coloring of a graph is a proper (vertex) coloring with the property that every vertex is either alone in its color class or adjacent to all vertices of at least one color class. A dominated coloring of a graph is a proper coloring such that every color class is dominated with at least one vertex. The dominator chromatic number of corona products and of edge corona products is determined. Sharp lower and upper bounds are given for the dominated chromatic number of edge corona products. The dominator chromatic number of hierarchical products is bounded from above and the dominated chromatic number of hierarchical products with two factors determined. An application of dominated colorings in genetic networks is also proposed.

Suggested Citation

  • Klavžar, Sandi & Tavakoli, Mostafa, 2021. "Dominated and dominator colorings over (edge) corona and hierarchical products," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    • Handle: RePEc:eee:apmaco:v:390:y:2021:i:c:s0096300320306019
    DOI: 10.1016/j.amc.2020.125647
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    References listed on IDEAS

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    1. Mostafa Tavakoli & Sandi Klavžar, 2019. "Distribution of global defensive k-alliances over some graph products," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(3), pages 615-623, September.
    2. Zhaoyang Luo & Jianliang Wu, 2014. "Zagreb Eccentricity Indices of the Generalized Hierarchical Product Graphs and Their Applications," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-8, February.
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    Cited by:

    1. Yangyang Zhou & Dongyang Zhao & Mingyuan Ma & Jin Xu, 2022. "Domination Coloring of Graphs," Mathematics, MDPI, vol. 10(6), pages 1-12, March.
    2. Shang, Yilun, 2022. "Sombor index and degree-related properties of simplicial networks," Applied Mathematics and Computation, Elsevier, vol. 419(C).

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