A nonzero integral flow f is conformally decomposable if \(f=f_1+f_2\), where \(f_1,f_2\) are nonzero integral flows, both are nonnegative or both are nonpositive. Conformally indecomposable flows on ordinary graphs are simply graph circuit flows. However, on signed graphs without outer-edges (compact case), conformally indecomposable flows, classified by Chen and Wang (arXiv:1112.0642, 2013) and by Chen et al. (Discret Math 340:1271–1286, 2017), are signed-graph circuit flows plus an extra class of characteristic flows of so-called Eulerian circle-trees. This paper is to classify indecomposable conformal integral flows on signed graphs with outer-edges (non-compact case). A notable feature is that with outer-edges the treatment is natural and results become stronger but proofs are simpler than that without outer-edges.

非零积分流f是共形可分解的，如果\(f=f_1+f_2\)，其中\(f_1,f_2\)是非零积分流，两者都是非负的或都是非正的。普通图上的共形不可分解流只是图电路流。然而，在没有外边的有符号图上（紧情况），共形不可分解流，由 Chen 和 Wang (arXiv:1112.0642, 2013) 以及 Chen 等人分类。(Discret Math 340:1271–1286, 2017)，是有符号图电路流加上所谓的欧拉圆树的额外特征流。本文旨在对带外边的有符号图（非紧致情况）上的不可分解保形积分流进行分类。一个显着的特点是，有外边缘的处理是自然的，结果变得更强，但证明比没有外边缘的更简单。