TY - JOUR
ID - 13779
TI - Lower bounds on the signed (total) $k$-domination number
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Volkmann, Lutz
AD - RWTH Aachen University
Y1 - 2018
PY - 2018
VL - 3
IS - 2
SP - 173
EP - 178
KW - signed $k$-dominating function
KW - signed $k$-domination number
KW - clique number
DO - 10.22049/cco.2018.26055.1071
N2 - 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.
UR - http://comb-opt.azaruniv.ac.ir/article_13779.html
L1 - http://comb-opt.azaruniv.ac.ir/article_13779_039e0161b2a16abce42b7a252a65cb4e.pdf
ER -