The 2-rainbow domination number of Cartesian bundles over cycles

Simon Brezovnik (), Darja Rupnik Poklukar () and Janez Žerovnik ()
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Simon Brezovnik: University of Ljubljana
Darja Rupnik Poklukar: University of Ljubljana
Janez Žerovnik: University of Ljubljana

Central European Journal of Operations Research, 2025, vol. 33, issue 3, No 2, 659 pages

Abstract: 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.

Keywords: 2-rainbow domination; Domination number; Graph bundles; 05C69; 05C76 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10100-024-00949-6

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