Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 11 3 2026 09 01 Weak signed double Roman domination in graphs 739 756 14871 10.22049/cco.2024.30016.2268 EN Lutz Volkmann RWTH Aachen University, 52056 Aachen, Germany Journal Article 2024 09 18 A weak signed double Roman dominating function (WSDRDF) of a graph $G$ with vertex set $V(G)$ is defined as a function $f:V(G)\rightarrow\{-1,1,2,3\}$ 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 WSDRDF is the sum of its function values over all vertices. The weak signed double Roman domination number of $G$, denoted by $\gamma_{wsdR}(G)$, is the minimum weight of a WSDRDF in $G$. We initiate the study of the weak signed double Roman domination number, and we present different sharp bounds on $\gamma_{wsdR}(G)$. In addition, we determine the weak signed double Roman domination number of some classes of graphs. https://comb-opt.azaruniv.ac.ir/article_14871_be0d2fde325e3b695f9f4ab3fec3dc9a.pdf