Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 11 4 2026 12 01 Weak signed total Italian domination in digraphs 1081 1091 15028 10.22049/cco.2025.30748.2606 EN Lutz Volkmann RWTH Aachen University, , 52056 Aachen, Germany Journal Article 2025 06 28 A weak signed total Italian dominating function (WSTIDF) of a digraph $D$ with vertex set $V(D)$ is defined as a<br />function $f:V(D)\rightarrow\{-1,1,2\}$ having the property that $\sum_{x\in N^-(v)}f(x)\ge 1$ for each $v\in V(D)$, where $N^-(v)$ consists of all vertices of $D$ from which arcs go into $v$. The weight of a WSTIDF is the sum of its function values over all vertices. The  weak signed total Italian domination number of $D$, denoted by $\gamma_{wstI}(D)$, is the minimum weight of a WSTIDF on $D$. We initiate the study of the weak signed total Italian domination number in digraphs, and we  present different sharp bounds on $\gamma_{wstI}(D)$. In addition, we determine the weak signed total Italian domination number of some classes of digraphs. https://comb-opt.azaruniv.ac.ir/article_15028_4163a82155762ca8713bd3d931ee079e.pdf