论文标题
概括基希霍夫法律的签名图
Generalizing Kirchhoff laws for Signed Graphs
论文作者
论文摘要
用于签名图的Kirchhoff型定律的特征是通过双向图的发病率结构概括了跨性别。 Tutte的经典$ 2 $ - ARBORESCENCE解释相当于单元素布尔的基于发病率的循环覆盖率，称为贡献者。使用自然在图中自然取消的整个布尔类别引入了广义贡献者传播。经典的保护被证明是微不足道的布尔班的财产。签名图上的贡献者转录显示出可产生非保守的Kirchhoff型法律，每个贡献者都具有独特的源链路路径属性。最后，通过无价的拉普拉斯计算贡献者传射的最大值。
Kirchhoff-type Laws for signed graphs are characterized by generalizing transpedances through the incidence-oriented structure of bidirected graphs. The classical $2$-arborescence interpretation of Tutte is shown to be equivalent to single-element Boolean classes of reduced incidence-based cycle covers, called contributors. A generalized contributor-transpedance is introduced using entire Boolean classes that naturally cancel in a graph; classical conservation is proven to be property of the trivial Boolean classes. The contributor-transpedances on signed graphs are shown to produce non-conservative Kirchhoff-type Laws, where every contributor possesses the unique source-sink path property. Finally, the maximum value of a contributor-transpedance is calculated through the signless Laplacian.
