@article {
author = {Volkmann, Lutz},
title = {Weak signed Roman domination in graphs},
journal = {Communications in Combinatorics and Optimization},
volume = {5},
number = {2},
pages = {111-123},
year = {2020},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2019.26598.1123},
abstract = {A weak signed Roman dominating function (WSRDF) of a graph $G$ with vertex set $V(G)$ is defined as a function $f:V(G)\rightarrow\{-1,1,2\}$ having the property that $\sum_{x\in N[v]}f(x)\ge 1$ for each $v\in V(G)$, where $N[v]$ is the closed 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.},
keywords = {domination,signed Roman domination,weak signed Roman domination},
url = {http://comb-opt.azaruniv.ac.ir/article_13989.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_13989_25818cd686d936e0f57852d8ce1b4284.pdf}
}