A Maximum Dicut in a Digraph Induced by a Minimal Dominating Set

Abstract

Let \(G = (V,A)\) be a simple directed graph and let \(S\subseteq V \) be a subset of the vertex set \(V \). The set \(S \) is called dominating if for each vertex \(j\in V\setminus S\) there exist at least one \(i\in S \) and an edge from \(i \) to \(j\). A dominating set is called (inclusion) minimal if it contains no smaller dominating set. A dicut \(\{S\rightarrow \overline {S}\} \) is a set of edges \((i,j)\in A \) such that \(i\in S \) and \(j\in V\setminus S \). The weight of a dicut is the total weight of all its edges. The article deals with the problem of finding a dicut \(\{S\rightarrow \overline {S}\} \) with maximum weight among all minimal dominating sets.

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Correspondence to V. V. Voroshilov.

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Translated by Ya.A. Kopylov

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Voroshilov, V.V. A Maximum Dicut in a Digraph Induced by a Minimal Dominating Set. J. Appl. Ind. Math. 14, 792–801 (2020). https://doi.org/10.1134/S199047892004016X

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Keywords

  • directed graph
  • weighted graph
  • maximum dicut
  • inclusion minimal dominating set