weak signed roman k-domatic number of a graph

let 𝑘⋝1 be an integer. a weak signed roman 𝑘-dominating function} on a graph 𝐺 isa function   ƒ:𝑉 (𝐺)→ {-1, 1, 2} such that ∑𝑢 ϵ 𝑁 [𝑣] ƒ(𝑢)⋝𝑘 for every 𝑣 ϵ𝑉(𝐺) , where 𝑁 [𝑣] is the closed neighborhood of v .a set {ƒ1,ƒ2,....,ƒ𝑑} of distinct weak signed roman 𝑘-dominatingfunctions on 𝐺 with the property that ∑𝑑𝑖=1 ƒ𝑖(𝑣)⋜ 𝑘 for each 𝑣 ϵ 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 𝑑𝑘ω𝑠𝑅(𝐺). in this paper we initiate the study of the weak signed roman 𝑘-domatic numberin graphs, and we present sharp bounds for 𝑑𝑘ω𝑠𝑅(𝐺) . in addition, we determine the weak signed roman𝑘-domatic number of some graphs.