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Weak signed total Italian domination in digraphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 22 مهر 1404 اصل مقاله (405.85 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30748.2606 | ||
| نویسنده | ||
| Lutz Volkmann* | ||
| RWTH Aachen University, , 52056 Aachen, Germany | ||
| چکیده | ||
| A weak signed total Italian dominating function (WSTIDF) of a digraph $D$ with vertex set $V(D)$ is defined as a 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. | ||
| کلیدواژهها | ||
| Digraphs؛ Weak signed total Italian domination؛ signed total Italian domination؛ signed total Roman domination؛ total domination | ||
| مراجع | ||
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