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...
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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 |
| _version_ | 1818790260682784768 |
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| author | M. Atapour A. Khodkar |
| author_facet | M. Atapour A. Khodkar |
| author_sort | M. Atapour |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-18T14:52:38Z |
| format | Article |
| id | doaj.art-546d14bd0d6e4aee8b444b41e71cf5ef |
| institution | Directory Open Access Journal |
| issn | 2538-2128 2538-2136 |
| language | English |
| last_indexed | 2024-12-18T14:52:38Z |
| publishDate | 2016-06-01 |
| publisher | Azarbaijan Shahide Madani University |
| record_format | Article |
| series | Communications in Combinatorics and Optimization |
| spelling | doaj.art-546d14bd0d6e4aee8b444b41e71cf5ef2022-12-21T21:04:07ZengAzarbaijan Shahide Madani UniversityCommunications in Combinatorics and Optimization2538-21282538-21362016-06-011214916410.22049/CCO.2016.13575Twin minus domination numbers in directed graphsM. Atapour0A. Khodkar1Dept. of Mathematics, Faculty of basic sciences, University of Bonab, Bonab, Iran Dept. of Mathematics, University of West Georgia, Carrollton, GA 30118, USALet $D=(V,A)$ 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.http://comb-opt.azaruniv.ac.ir/article_13575.htmlTwin domination in digraphsminus domination in graphs twin minus domination in digraphs |
| spellingShingle | M. Atapour A. Khodkar Twin minus domination numbers in directed graphs Communications in Combinatorics and Optimization Twin domination in digraphs minus domination in graphs twin minus domination in digraphs |
| title | Twin minus domination numbers in directed graphs |
| title_full | Twin minus domination numbers in directed graphs |
| title_fullStr | Twin minus domination numbers in directed graphs |
| title_full_unstemmed | Twin minus domination numbers in directed graphs |
| title_short | Twin minus domination numbers in directed graphs |
| title_sort | twin minus domination numbers in directed graphs |
| topic | Twin domination in digraphs minus domination in graphs twin minus domination in digraphs |
| url | http://comb-opt.azaruniv.ac.ir/article_13575.html |
| work_keys_str_mv | AT matapour twinminusdominationnumbersindirectedgraphs AT akhodkar twinminusdominationnumbersindirectedgraphs |