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Weak signed total Italian domination in graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 18، دوره 12، شماره 1، خرداد 2027، صفحه 283-296 اصل مقاله (436.94 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30397.2451 | ||
| نویسنده | ||
| Lutz Volkmann* | ||
| RWTH Aachen University, 52056 Aachen, Germany | ||
| چکیده | ||
| A weak signed total Italian dominating function (WSTIDF) of a graph $G$ with vertex set $V(G)$ is defined as a function $f:V(G)\rightarrow\{-1,1,2\}$ having the property that $\sum_{x\in N(v)}f(x)\ge 1$ for each $v\in V(G)$, where $N(v)$ is the neighborhood of $v$. The weight of a WSTIDF is the sum of its function values over all vertices. The weak signed total Italian domination number of $G$, denoted by $\gamma_{wstI}(G)$, is the minimum weight of a WSTIDF in $G$. We initiate the study of the weak signed total Italian domination number, and we present different sharp bounds on $\gamma_{wstI}(G)$. In addition, we determine the weak signed total Italian domination number of some classes of graphs. | ||
| کلیدواژهها | ||
| weak signed total Italian domination؛ signed total Italian domination؛ signed total Roman domination؛ total domination | ||
| مراجع | ||
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