Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21285220201201Weak signed Roman domination in graphs1111231398910.22049/cco.2019.26598.1123ENLutzVolkmannRWTH Aachen University0000-0003-3496-277XJournal Article20190625A {em weak signed Roman dominating function} (WSRDF) of a graph $G$ with vertex set $V(G)$ is defined as a<br />function $f:V(G)rightarrow{-1,1,2}$ having the property that $sum_{xin N[v]}f(x)ge 1$ for each $vin V(G)$, where $N[v]$ is the<br />closed neighborhood of $v$. The weight of a WSRDF is the sum of its function values over all vertices.<br />The weak signed Roman domination number of $G$, denoted by $gamma_{wsR}(G)$, is the minimum weight of a WSRDF in $G$.<br />We initiate the study of the weak signed Roman domination number, and we present different sharp bounds on $gamma_{wsR}(G)$.<br />In addition, we determine the weak signed Roman domination number of some classes of graphs.http://comb-opt.azaruniv.ac.ir/article_13989_25818cd686d936e0f57852d8ce1b4284.pdf