Weak signed Roman domination in graphs

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.