A signed edge-domination of graph G is a function \(f:\ E(G)\rightarrow \{+1,-1\}\) such that \(\sum _{e'\in N_{G}[e]}{f(e')}\ge 1\) for each \(e\in E(G)\). A set \(\{ f_1,f_2,\ldots , f_d \}\) of the signed edge-domination of G is called a family of signed edge-dominations of G if \(\sum _{i=1}^{d}{f_i(e)}\le 1 \) for every \(e \in E(G)\). 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.

中文翻译：

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近三次图的有符号边域数

图G的有符号边支配是一个函数\(f:\ E(G)\rightarrow \{+1,-1\}\)使得\(\sum _{e'\in N_{G}[ e]}{f(e')}\ge 1\)对于每个\(e\in E(G)\)。如果\ ( \ sum _ { i=1} ^ { d}{f_i(e)}\le 1 \)对于每个\(e \in E(G)\)。G的有符号边支配族的最大数是G的有符号边支配数. 本文研究了近三次图的有符号边域数，并为一类图确定了该参数。