Geodesic
A~maximum dicut in~a~digraph induced by~a~minimal~dominating~set
Diskretnyj analiz i issledovanie operacij, Tome 27 (2020) no. 4, pp. 5-20

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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 $\overline{S}$ 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 $\overline{S}$ with maximum weight among all minimal dominating sets. Illustr. 6, bibliogr. 8.
Keywords: directed graph, weighted graph, maximum dicut, inclusion minimal dominating set. 
@article{DA_2020_27_4_a0,
     author = {V. V. Voroshilov},
     title = {A~maximum dicut in~a~digraph induced by~a~minimal~dominating~set},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {5--20},
     publisher = {mathdoc},
     volume = {27},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2020_27_4_a0/}
}
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V. V. Voroshilov. A~maximum dicut in~a~digraph induced by~a~minimal~dominating~set. Diskretnyj analiz i issledovanie operacij, Tome 27 (2020) no. 4, pp. 5-20. http://geodesic.mathdoc.fr/item/DA_2020_27_4_a0/