Twin minus domination numbers in directed graphs
Let $D=(V,A)$ be a finite simple directed graph. A function $f:V\longrightarrow \{-1,0,1\}$ is called a twin minus dominating function if $f(N^-[v])\ge 1$ and $f(N^+[v])\ge 1$ for each vertex $v\in V$. The twin minus domination number of $D$ is $\gamma_{-}^*(D)=\min\{w(f)\mid f \mbo...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Azarbaijan Shahide Madani University
2016-06-01
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| Series: | Communications in Combinatorics and Optimization |
| Subjects: | |
| Online Access: | http://comb-opt.azaruniv.ac.ir/article_13575.html |
| Summary: | Let $D=(V,A)$ be a finite simple directed graph. A
function $f:V\longrightarrow \{-1,0,1\}$ is called a twin minus
dominating function if $f(N^-[v])\ge 1$ and $f(N^+[v])\ge
1$ for each vertex $v\in V$. The twin minus domination number of
$D$ is $\gamma_{-}^*(D)=\min\{w(f)\mid f \mbox{ is a twin minus
dominating function of }
D\}$. In this paper, we initiate the study of twin minus
domination numbers in digraphs and present some lower bounds for
$\gamma_{-}^*(D)$ in terms of the order, size and maximum and
minimum in-degrees and out-degrees. |
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| ISSN: | 2538-2128 2538-2136 |