A signed graph is a pair \((G,\tau )\) of a graph G and its sign \(\tau \), where a sign \(\tau \) is a function from \(\{ (e,v)\mid e\in E(G),v\in V(G), v\in e\}\) to \(\{1,-1\}\). Note that graphs or digraphs are special cases of signed graphs. In this paper, we study the toric ideal \(I_{(G,\tau )}\) associated with a signed graph \((G,\tau )\), and the results of the paper give a unified idea to explain some known results on the toric ideals of a graph or a digraph. We characterize all primitive binomials of \(I_{(G,\tau )}\) and then focus on the complete intersection property. More precisely, we find a complete list of graphs G such that \(I_{(G,\tau )}\) is a complete intersection for every sign \(\tau \).

有符号图是图G及其符号\（\ tau \）的一对\（（G，\ tau）\），其中符号\（\ tau \）是\（\ {（e， v）\ mid e \在E（G）中，v \在V（G）中，v \在e \} \）到\（\ {1，-1 \} \）。请注意，图或有向图是带符号图的特殊情况。在本文中，我们研究了与有符号图\（（G，\ tau）\）关联的复曲面理想\（I _ {（G，\ tau）} \），并且论文的结果给出了统一的思想来解释关于图或有向图的复曲面理想的一些已知结果。我们表征\（I _ {（G，\ tau）} \）的所有原始二项式 然后专注于完整的交集属性。更准确地说，我们找到了图G的完整列表，使得\（I _ {（G，\ tau）} \）是每个符号\（\ tau \）的完整交集。