@article {
author = {Volkmann, Lutz},
title = {Weak signed Roman k-domatic number of a graph},
journal = {Communications in Combinatorics and Optimization},
volume = {7},
number = {1},
pages = {17-27},
year = {2022},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2021.26998.1178},
abstract = {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.},
keywords = {weak signed Roman k-dominating function,weak signed Roman k-domination number,weak signed Roman k-domatic number},
url = {http://comb-opt.azaruniv.ac.ir/article_14169.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_14169_1e588e4245ba97d8d37a13423c97b545.pdf}
}