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Integer linear programming models for the weighted total domination problem

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  • Ma, Yuede
  • Cai, Qingqiong
  • Yao, Shunyu

Abstract

A total dominating set of a graph G=(V,E) is a subset D of V such that every vertex in V (including the vertices from D) has at least one neighbour in D. Suppose that every vertex v ∈ V has an integer weight w(v) ≥ 0 and every edge e ∈ E has an integer weight w(e) ≥ 0. Then the weighted total domination (WTD) problem is to find a total dominating set D which minimizes the cost f(D):=∑u∈Dw(u)+∑e∈E[D]w(e)+∑v∈V∖Dmin{w(uv)|u∈N(v)∩D}. In this paper, we put forward three integer linear programming (ILP) models with a polynomial number of constraints, and present some numerical results implemented on random graphs for WTD problem.

Suggested Citation

  • Ma, Yuede & Cai, Qingqiong & Yao, Shunyu, 2019. "Integer linear programming models for the weighted total domination problem," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 146-150.
    • Handle: RePEc:eee:apmaco:v:358:y:2019:i:c:p:146-150
    DOI: 10.1016/j.amc.2019.04.038
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    References listed on IDEAS

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    1. Chen, Lily & Ma, Yingbin & Shi, Yongtang & Zhao, Yan, 2018. "On the [1,2]-domination number of generalized Petersen graphs," Applied Mathematics and Computation, Elsevier, vol. 327(C), pages 1-7.
    2. Yue, Jun & Wei, Meiqin & Li, Min & Liu, Guodong, 2018. "On the double Roman domination of graphs," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 669-675.
    3. Pinacho Davidson, Pedro & Blum, Christian & Lozano, Jose A., 2018. "The weighted independent domination problem: Integer linear programming models and metaheuristic approaches," European Journal of Operational Research, Elsevier, vol. 265(3), pages 860-871.
    4. Yongtang Shi & Meiqin Wei & Jun Yue & Yan Zhao, 2017. "Coupon coloring of some special graphs," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 156-164, January.
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