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Independent Rainbow Domination Numbers of Generalized Petersen Graphs P ( n ,2) and P ( n ,3)

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  • Boštjan Gabrovšek

    (FME, University of Ljubljana, Aškerčeva 6, SI-1000 Ljubljana, Slovenia
    IMFM, Jadranska 19, SI-1000 Ljubljana, Slovenia)

  • Aljoša Peperko

    (FME, University of Ljubljana, Aškerčeva 6, SI-1000 Ljubljana, Slovenia
    IMFM, Jadranska 19, SI-1000 Ljubljana, Slovenia)

  • Janez Žerovnik

    (FME, University of Ljubljana, Aškerčeva 6, SI-1000 Ljubljana, Slovenia
    IMFM, Jadranska 19, SI-1000 Ljubljana, Slovenia)

Abstract

We obtain new results on independent 2- and 3-rainbow domination numbers of generalized Petersen graphs P ( n , k ) for certain values of n , k ∈ N . By suitably adjusting and applying a well established technique of tropical algebra (path algebra) we obtain exact 2-independent rainbow domination numbers of generalized Petersen graphs P ( n , 2 ) and P ( n , 3 ) thus confirming a conjecture proposed by Shao et al. In addition, we compute exact 3-independent rainbow domination numbers of generalized Petersen graphs P ( n , 2 ) . The method used here is developed for rainbow domination and for Petersen graphs. However, with some natural modifications, the method used can be applied to other domination type invariants, and to many other classes of graphs including grids and tori.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:996-:d:373042
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    References listed on IDEAS

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    1. 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.
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