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Generalizing Kirchhoff laws for Signed Graphs
- Publication Year :
- 2020
-
Abstract
- 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.<br />Comment: 22 pages, 16 figures
- Subjects :
- Mathematics - Combinatorics
05C22, 05C05, 05C50, 05B20, 05B45
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2009.12680
- Document Type :
- Working Paper