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- Title
Algorithmic aspect on total Roman {2}-domination of Cartesian products of paths and cycles.
- Authors
Chen, Qin
- Abstract
A total Roman {2}-dominating function (TR2DF) on a graph G with vertex set V is a function f : V → {0, 1, 2} having the property that for every vertex v with f(v) = 0, ∑u∈N (v)f(u) ≥ 2, where N(v) represents the open neighborhood of v, and the subgraph of G induced by the set of vertices with f(v) > 0 has no isolated vertex. The weight of a TR2DF f is the value w(f) = ∑v∈Vf(v), and the minimum weight of a TR2DF of G is the total Roman {2}-domination number γtR2(G). The total Roman {2}-domination problem (TR2DP) is to determine the value γtR2(G). In this paper, we first propose an integer linear programming (ILP) formulation for the TR2DP. Furthermore, we apply the discharging approach to determine the total Roman {2}-domination number for some Cartesian products of paths and cycles.
- Subjects
DOMINATING set; LINEAR programming; INTEGER programming; ROMANS
- Publication
RAIRO: Operations Research (2804-7303), 2024, Vol 58, Issue 2, p2029
- ISSN
2804-7303
- Publication type
Article
- DOI
10.1051/ro/2023121