Weak signed total Italian domination in graphs

	Weak signed total Italian domination in graphs
Communications in Combinatorics and Optimization
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 01 فروردین 1404 اصل مقاله (412.73 K)
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2025.30397.2451
نویسنده
Lutz Volkmann^*
RWTH Aachen University
چکیده
A {\em 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 {\em 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

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