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Algebra and Discrete Mathematics, 2017, Volume 24, Issue 1, Pages 71–89
(Mi adm619)
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This article is cited in 2 scientific papers (total in 2 papers)
Twin signed domination numbers in directed graphs
M. Atapoura, S. Norouzianb, S. M. Sheikholeslamib, L. Volkmannc a Department of Mathematics, University of Bonab, Bonab, I.R. Iran
b Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran
c RWTH Aachen University, 52056 Aachen, Germany
Abstract:
Let $D=(V,A)$ be a finite simple directed graph (shortly digraph). A function $f\colon V\to \{-1,1\}$ is called a twin signed dominating function (TSDF) if $f(N^-[v])\ge 1$ and $f(N^+[v])\ge 1$ for each vertex $v\in V$. The twin signed domination number of $D$ is $\gamma_{s}^*(D)=\min\{\omega(f)\mid f \text{ is a TSDF of } D\}$. In this paper, we initiate the study of twin signed domination in digraphs and we present sharp lower bounds for $\gamma_{s}^*(D)$ in terms of the order, size and maximum and minimum indegrees and outdegrees. Some of our results are extensions of well-known lower bounds of the classical signed domination numbers of graphs.
Keywords:
twin signed dominating function, twin signed domination number, directed graph.
Received: 21.09.2015 Revised: 10.11.2015
Citation:
M. Atapour, S. Norouzian, S. M. Sheikholeslami, L. Volkmann, “Twin signed domination numbers in directed graphs”, Algebra Discrete Math., 24:1 (2017), 71–89
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https://www.mathnet.ru/eng/adm619 https://www.mathnet.ru/eng/adm/v24/i1/p71
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Abstract page: | 133 | Full-text PDF : | 93 | References: | 35 |
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