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ЖУРНАЛЫ // Algebra and Discrete Mathematics // Архив

Algebra Discrete Math., 2017, том 24, выпуск 1, страницы 71–89 (Mi adm619)

Эта публикация цитируется в 2 статьях

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

Аннотация: 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.

Ключевые слова: twin signed dominating function, twin signed domination number, directed graph.

MSC: 05C69

Поступила в редакцию: 21.09.2015
Исправленный вариант: 10.11.2015

Язык публикации: английский



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