@article {
author = {Volkmann, Lutz},
title = {Lower bounds on the signed (total) $k$-domination number},
journal = {Communications in Combinatorics and Optimization},
volume = {3},
number = {2},
pages = {173-178},
year = {2018},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2018.26055.1071},
abstract = {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.},
keywords = {signed $k$-dominating function,signed $k$-domination number,clique number},
url = {http://comb-opt.azaruniv.ac.ir/article_13779.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_13779_039e0161b2a16abce42b7a252a65cb4e.pdf}
}