The signed edge-domatic number of nearly cubic graphs

A signed edge-domination of graph G is a function $$f:\ E(G)\rightarrow \{+1,-1\}$$ f : E ( G ) → { + 1 , - 1 } such that $$\sum _{e'\in N_{G}[e]}{f(e')}\ge 1$$ ∑ e ′ ∈ N G [ e ] f ( e ′ ) ≥ 1 for each $$e\in E(G)$$ e ∈ E ( G ) . A set $$\{ f_1,f_2,\ldots , f_d \}$$ { f 1 , f 2 , … , f d } of the signed edge-domination of G is called a family of signed edge-dominations of G if $$\sum _{i=1}^{d}{f_i(e)}\le 1 $$ ∑ i = 1 d f i ( e ) ≤ 1 for every $$e \in E(G)$$ e ∈ E ( G ) . The largest number of a family of signed edge-dominations of G is the signed edge-domatic number of G. This paper studies the signed edge-domatic number of nearly cubic graph, and determines this parameter for a class of graphs.