%0 Journal Article %T Weak signed Roman k-domatic number of a graph %J Communications in Combinatorics and Optimization %I Azarbaijan Shahid Madani University %Z 2538-2128 %A Volkmann, Lutz %D 2022 %\ 06/01/2022 %V 7 %N 1 %P 17-27 %! Weak signed Roman k-domatic number of a graph %K weak signed Roman k-dominating function %K weak signed Roman k-domination number %K weak signed Roman k-domatic number %R 10.22049/cco.2021.26998.1178 %X Let $k\ge 1$ be an integer. A { weak signed Roman $k$-dominating function} on a graph $G$ isa 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 $k$-dominatingfunctions 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 functionsin 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 numberin 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. %U http://comb-opt.azaruniv.ac.ir/article_14169_1e588e4245ba97d8d37a13423c97b545.pdf