Uniform Kirchhoff graphs
| Autor: | Tyler M. Reese, Joseph D. Fehribach, Brigitte Servatius, Randy Paffenroth |
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| Rok vydání: | 2019 |
| Předmět: |
Discrete mathematics
Numerical Analysis Algebra and Number Theory Assignment function 010102 general mathematics Incidence matrix Digraph Characteristic matrix 010103 numerical & computational mathematics 01 natural sciences Graph Matrix (mathematics) Vector graphics Computer Science::Emerging Technologies Discrete Mathematics and Combinatorics Geometry and Topology 0101 mathematics Mathematics |
| Zdroj: | Linear Algebra and its Applications. 566:1-16 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2018.12.018 |
| Popis: | This paper presents an entirely linear-algebraic interpretation of Kirchhoff graphs. Specifically, whether or not a vector graph is Kirchhoff can be determined using only the incidence matrix of the underlying digraph, and the characteristic matrix of the vector assignment function. This is then used to classify the families of matrices for which any Kirchhoff graph must be uniform, in the sense that the vector edges all occur the same number of times. Next, we demonstrate that any matrix having a Kirchhoff graph must always have a uniform example. Finally, we introduce a notion of 2-connectedness of vector graphs, and show that every 2-connected Kirchhoff graph must be uniform. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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