%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 $kge 1$ 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 $sum_{uin N[v]}f(u)ge k$ for every$vin V(G)$, 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 $vin V(G)$, 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