Volkmann, L. (2018). Lower bounds on the signed (total) $k$-domination number. Communications in Combinatorics and Optimization, 3(2), 173-178. doi: 10.22049/cco.2018.26055.1071

Lutz Volkmann. "Lower bounds on the signed (total) $k$-domination number". Communications in Combinatorics and Optimization, 3, 2, 2018, 173-178. doi: 10.22049/cco.2018.26055.1071

Volkmann, L. (2018). 'Lower bounds on the signed (total) $k$-domination number', Communications in Combinatorics and Optimization, 3(2), pp. 173-178. doi: 10.22049/cco.2018.26055.1071

Volkmann, L. Lower bounds on the signed (total) $k$-domination number. Communications in Combinatorics and Optimization, 2018; 3(2): 173-178. doi: 10.22049/cco.2018.26055.1071

Lower bounds on the signed (total) $k$-domination number

Let $G$ be a graph with vertex set $V(G)$. For any integer $kge 1$, a signed (total) $k$-dominating function is a function $f: V(G) rightarrow { -1, 1}$ satisfying $sum_{xin N[v]}f(x)ge k$ ($sum_{xin N(v)}f(x)ge k$) for every $vin V(G)$, where $N(v)$ is the neighborhood of $v$ and $N[v]=N(v)cup{v}$. The minimum of the values $sum_{vin V(G)}f(v)$, 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.