The minus $k$-domination numbers in graphs
For any integer $k\ge 1$, a minus $k$-dominating function is a function $f : V \rightarrow \{-1,0, 1\}$ satisfying $\sum_{w\in N[v]} f(w)\ge k$ for every $v\in V(G)$, where $N(v) =\{u \in V(G)\mid uv\in E(G)\}$ and $N[v] =N(v)\cup \{v\}$. The minimum of the values of $\sum_{v\in V(G)}f(v)$...
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| Format: | Article |
| Language: | English |
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Azarbaijan Shahide Madani University
2016-01-01
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| Series: | Communications in Combinatorics and Optimization |
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| Online Access: | http://comb-opt.azaruniv.ac.ir/article_13534_2212.html |
| Summary: | For any integer $k\ge 1$, a minus $k$-dominating function is a function $f : V \rightarrow \{-1,0, 1\}$ satisfying $\sum_{w\in N[v]} f(w)\ge k$ for every $v\in V(G)$, where $N(v) =\{u \in V(G)\mid uv\in E(G)\}$ and $N[v] =N(v)\cup \{v\}$. The minimum of the values of $\sum_{v\in V(G)}f(v)$, taken over all minus
$k$-dominating functions $f$, is called the minus $k$-domination number and is denoted by $\gamma^-_{k}(G)$. In this paper, we introduce the study of minus $k$-domination in graphs and present several sharp lower bounds on the minus $k$-domination number for general graphs. |
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| ISSN: | 2538-2128 2538-2136 |