In 2020, Behr defined the problem of edge coloring of signed graphs and showed that every signed graph $(G, \sigma)$ can be colored using exactly $\Delta(G)$ or $\Delta(G) + 1$ colors, where $\Delta(G)$ is the maximum degree in graph $G$. In this paper, we focus on products of signed graphs. We recall the definitions of the Cartesian, tensor, strong, and corona products of signed graphs and prove results for them. In particular, we show that $(1)$ the Cartesian product of $\Delta$-edge-colorable signed graphs is $\Delta$-edge-colorable, $(2)$ the tensor product of a $\Delta$-edge-colorable signed graph and a signed tree requires only $\Delta$ colors and $(3)$ the corona product of almost any two signed graphs is $\Delta$-edge-colorable. We also prove some results related to the coloring of products of signed paths and cycles.

翻译：2020年，Behr定义了带符号图的边着色问题，并证明了每个带符号图$(G, \sigma)$均可使用恰好$\Delta(G)$或$\Delta(G) + 1$种颜色着色，其中$\Delta(G)$为图$G$中的最大度。本文聚焦于带符号图的乘积。我们回顾了带符号图的笛卡尔积、张量积、强积和冠状积的定义，并证明了相关结论。特别地，我们证明了：$(1)$ $\Delta$-边可着色带符号图的笛卡尔积是$\Delta$-边可着色的；$(2)$ 一个$\Delta$-边可着色带符号图与一个带符号树的张量积仅需$\Delta$种颜色；$(3)$ 几乎任意两个带符号图的冠状积是$\Delta$-边可着色的。我们还证明了与带符号路径和带符号圈的乘积着色相关的一些结论。