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Signed total Italian $k$-domination in digraphs | ||
| Communications in Combinatorics and Optimization | ||
| دوره 9، شماره 2، شهریور 2024، صفحه 339-351 اصل مقاله (409.27 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.27872.1377 | ||
| نویسنده | ||
| Lutz Volkmann* | ||
| RWTH Aachen University | ||
| چکیده | ||
| Let $k\ge 1$ be an integer, and let $D$ be a finite and simple digraph with vertex set $V(D)$. A signed total Italian $k$-dominating function (STIkDF) on a digraph $D$ is a function $f:V(D)\rightarrow\{-1,1,2\}$ satisfying the conditions that (i) $\sum_{x\in N^-(v)}f(x)\ge k$ for each vertex $v\in V(D)$, where $N^-(v)$ consists of all vertices of $D$ from which arcs go into $v$, and (ii) each vertex $u$ with $f(u)=-1$ has an in-neighbor $v$ for which $f(v)=2$ or two in-neighbors $w$ and $z$ with $f(w)=f(z)=1$. The weight of an STIkDF $f$ is $\omega(f)=\sum_{v\in V(D)}f(v)$. The signed total Italian $k$-domination number $\gamma_{stI}^k(D)$ of $D$ is the minimum weight of an STIkDF on $D$. In this paper we initiate the study of the signed total Italian $k$-domination number of digraphs, and we present different bounds on $\gamma_{stI}^k(D)$. In addition, we determine the signed total Italian $k$-domination number of some classes of digraphs. | ||
| کلیدواژهها | ||
| Digraph؛ Signed total Italian $k$-dominating function؛ Signed total Italian $k$-domination number؛ Signed total Roman $k$-dominating function؛ Signed total Roman $k$-domination number | ||
| مراجع | ||
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