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 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. UR - http://comb-opt.azaruniv.ac.ir/article_13989.html L1 - http://comb-opt.azaruniv.ac.ir/article_13989_25818cd686d936e0f57852d8ce1b4284.pdf ER -