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Weak signed Roman k-domatic number of a graph | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 2، دوره 7، شماره 1، شهریور 2022، صفحه 17-27 اصل مقاله (378.5 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2021.26998.1178 | ||
| نویسنده | ||
| Lutz Volkmann* | ||
| RWTH Aachen University | ||
| چکیده | ||
| Let $k\ge 1$ be an integer. A { weak signed Roman $k$-dominating function} on a graph $G$ is a function $f:V (G)\longrightarrow \{-1, 1, 2\}$ such that $\sum_{u\in N[v]}f(u)\ge k$ for every $v\in V(G)$, where $N[v]$ is the closed neighborhood of $v$. A set $\{f_1,f_2,\ldots,f_d\}$ of distinct weak signed Roman $k$-dominating functions on $G$ with the property that $\sum_{i=1}^df_i(v)\le k$ for each $v\in V(G)$, is called a { weak signed Roman $k$-dominating family} (of functions) on $G$. The maximum number of functions in a weak signed Roman $k$-dominating family on $G$ is the { weak signed Roman $k$-domatic number} of $G$, denoted by $d_{wsR}^k(G)$. In this paper we initiate the study of the weak signed Roman $k$-domatic number in graphs, and we present sharp bounds for $d_{wsR}^k(G)$. In addition, we determine the weak signed Roman $k$-domatic number of some graphs. | ||
| کلیدواژهها | ||
| weak signed Roman k-dominating function؛ weak signed Roman k-domination number؛ weak signed Roman k-domatic number | ||
| مراجع | ||
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