TY - JOUR
ID - 13989
TI - Weak signed Roman domination in graphs
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Volkmann, Lutz
AD - RWTH Aachen University
Y1 - 2020
PY - 2020
VL - 5
IS - 2
SP - 111
EP - 123
KW - domination
KW - signed Roman domination
KW - weak signed Roman domination
DO - 10.22049/cco.2019.26598.1123
N2 - A {em weak signed Roman dominating function} (WSRDF) of a graph $G$ with vertex set $V(G)$ is defined as afunction $f:V(G)rightarrow{-1,1,2}$ having the property that $sum_{xin N[v]}f(x)ge 1$ for each $vin V(G)$, where $N[v]$ is theclosed neighborhood of $v$. The weight of a WSRDF is the sum of its function values over all vertices.The weak signed Roman domination number of $G$, denoted by $gamma_{wsR}(G)$, is the minimum weight of a WSRDF in $G$.We initiate the study of the weak signed Roman domination number, and we present different sharp bounds on $gamma_{wsR}(G)$.In addition, we determine the weak signed Roman domination number of some classes of graphs.
UR - http://comb-opt.azaruniv.ac.ir/article_13989.html
L1 - http://comb-opt.azaruniv.ac.ir/article_13989_25818cd686d936e0f57852d8ce1b4284.pdf
ER -