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The 2-rainbow domination number of Cartesian bundles over cycles

Author

Listed:
  • Simon Brezovnik

    (University of Ljubljana
    Institute of Mathematics, Physics, and Mechanics)

  • Darja Rupnik Poklukar

    (University of Ljubljana)

  • Janez Žerovnik

    (University of Ljubljana
    Rudolfovo - Science and Technology Centre)

Abstract

A k-rainbow dominating function (kRDF) f of G assigns subsets of $$\{1,2,\ldots ,k\}$$ { 1 , 2 , … , k } to vertices, such that for vertex v with $$f(v)=\emptyset$$ f ( v ) = ∅ , $$\bigcup \nolimits _{u\in N(v)}f(u)=\{1,2,\ldots ,k\}$$ ⋃ u ∈ N ( v ) f ( u ) = { 1 , 2 , … , k } . The weight w(f) of kRDF f is $$w(f)=\sum _{v\in V(G)}\left| f(v)\right|$$ w ( f ) = ∑ v ∈ V ( G ) f ( v ) . The minimum weight of a kRDF of G is the k-rainbow domination number denoted by $$\gamma _{rk}(G)$$ γ rk ( G ) . This paper focuses on the 2-rainbow domination number of Cartesian graph bundles of cycles over cycles, extending recent results for Cartesian product of cycles. Exact values are given for certain infinite families, and tight lower and upper bounds are established for general case.

Suggested Citation

  • Simon Brezovnik & Darja Rupnik Poklukar & Janez Žerovnik, 2025. "The 2-rainbow domination number of Cartesian bundles over cycles," 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. 33(3), pages 641-659, September.
  • Handle: RePEc:spr:cejnor:v:33:y:2025:i:3:d:10.1007_s10100-024-00949-6
    DOI: 10.1007/s10100-024-00949-6
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