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Weak signed Roman $k$-domatic number of a digraph | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 30 مرداد 1403 اصل مقاله (429.05 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29074.1834 | ||
| نویسنده | ||
| Lutz Volkmann* | ||
| RWTH Aachen University, 52056 Aachen, Germany | ||
| چکیده | ||
| Let $D$ be a digraph with vertex set $V(D)$, and let $k\ge 1$ be an integer. A weak signed Roman $k$-dominating function on a digraph $D$ is a function $f:V (D)\longrightarrow \{-1, 1, 2\}$ such that $\sum_{u\in N^-[v]}f(u)\ge k$ for every $v\in V(D)$, where $N^-[v]$ consists of $v$ and all vertices of $D$ from which arcs go into $v$. A set $\{f_1,f_2,\ldots,f_d\}$ of distinct weak signed Roman $k$-dominating functions on $D$ with the property that $\sum_{i=1}^df_i(v)\le k$ for each $v\in V(D)$, is called a weak signed Roman $k$-dominating family (of functions) on $D$. The maximum number of functions in a weak signed Roman $k$-dominating family on $D$ is the weak signed Roman $k$-domatic number of $D$, denoted by $d_{wsR}^k(D)$. In this paper we initiate the study of the weak signed Roman $k$-domatic number in digraphs, and we present sharp bounds for $d_{wsR}^k(D)$. In addition, we determine the weak signed Roman $k$-domatic number of some digraphs. | ||
| کلیدواژه‌ها | ||
| digraphs؛ weak signed Roman $k$-dominating function؛ weak signed Roman $k$-domination number؛ weak signed Roman $k$-domatic number | ||
| مراجع | ||
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