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Abstract: A k-rainbow dominating function (kRDF) of G is a function that assigns subsets of {1, 2, ..., k} to the vertices of G such that for vertices v with f(v) = ∅ we have ⋃{u ∈ N(v)}f(u) = {1, 2, ..., k}. The weight w(f) of a kRDF f is defined as w(f) = ∑{v ∈ V(G)}|f(v)|. The minimum weight of a kRDF of G is called the k-rainbow domination number of G, which is denoted by γrk(G). In this paper, we study the 2-rainbow domination number of the Cartesian product of two cycles. Exact values are given for a number of infinite families and we prove lower and upper bounds for all other cases.
Keywords: 2-rainbow domination, domination number, Cartesian product
Published in RUP: 21.10.2025; Views: 383; Downloads: 5
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