Lower bounds on the signed (total) $k$-domination number depending on the clique number
| Autor: | L. Volkmann |
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| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Communications in Combinatorics and Optimization, Vol 3, Iss 2, Pp 173-178 (2018) |
| Druh dokumentu: | article |
| ISSN: | 2538-2128 2538-2136 |
| DOI: | 10.22049/CCO.2018.26055.1071 |
| Popis: | Let $G$ be a graph with vertex set $V(G)$. For any integer $k\ge 1$, a signed (total) $k$-dominating function is a function $f: V(G) \rightarrow \{ -1, 1\}$ satisfying $\sum_{x\in N[v]}f(x)\ge k$ ($\sum_{x\in N(v)}f(x)\ge k$) for every $v\in V(G)$, where $N(v)$ is the neighborhood of $v$ and $N[v]=N(v)\cup\{v\}$. The minimum of the values $\sum_{v\in V(G)}f(v)$, taken over all signed (total) $k$-dominating functions $f$, is called the signed (total) $k$-domination number. The clique number of a graph $G$ is the maximum cardinality of a complete subgraph of $G$. In this note we present some new sharp lower bounds on the signed (total) $k$-domination number depending on the clique number of the graph. Our results improve some known bounds. |
| Databáze: | Directory of Open Access Journals |
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