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On k-rainbow independent domination in graphs

Author

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  • Kraner Šumenjak, Tadeja
  • Rall, Douglas F.
  • Tepeh, Aleksandra

Abstract

In this paper, we define a new domination invariant on a graph G, which coincides with the ordinary independent domination number of the generalized prism G□Kk, called the k-rainbow independent domination number and denoted by γrik(G). Some bounds and exact values concerning this domination concept are determined. As a main result, we prove a Nordhaus–Gaddum-type theorem on the sum for 2-rainbow independent domination number, and show if G is a graph of order n ≥ 3, then 5≤γri2(G)+γri2(G¯)≤n+3, with both bounds being sharp.

Suggested Citation

  • Kraner Šumenjak, Tadeja & Rall, Douglas F. & Tepeh, Aleksandra, 2018. "On k-rainbow independent domination in graphs," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 353-361.
    • Handle: RePEc:eee:apmaco:v:333:y:2018:i:c:p:353-361
    DOI: 10.1016/j.amc.2018.03.113
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    References listed on IDEAS

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    1. Du, Zhibin, 2017. "Further results regarding the sum of domination number and average eccentricity," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 299-309.
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    Cited by:

    1. Brezovnik, Simon & Šumenjak, Tadeja Kraner, 2019. "Complexity of k-rainbow independent domination and some results on the lexicographic product of graphs," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 214-220.
    2. Enqiang Zhu, 2021. "An Improved Nordhaus–Gaddum-Type Theorem for 2-Rainbow Independent Domination Number," Mathematics, MDPI, vol. 9(4), pages 1-10, February.
    3. Boštjan Gabrovšek & Aljoša Peperko & Janez Žerovnik, 2020. "Independent Rainbow Domination Numbers of Generalized Petersen Graphs P ( n ,2) and P ( n ,3)," Mathematics, MDPI, vol. 8(6), pages 1-13, June.

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    1. Brezovnik, Simon & Šumenjak, Tadeja Kraner, 2019. "Complexity of k-rainbow independent domination and some results on the lexicographic product of graphs," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 214-220.
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