A combinatorial proof of the Rayleigh formula for graphs
- Title
- A combinatorial proof of the Rayleigh formula for graphs
- Authors
- Choe, YoungBin; null
- Date Issued
- 2008-01
- Publisher
- .
- Abstract
- Rayleigh monotonicity in Physics has a combinatorial interpretation. In this paper we give a combinatorial proof of the Rayleigh formula using the Jacobi Identity and the all-minors matrix tree Theorem. Motivated by the fact that the edge set of each spanning tree of G is a basis of the graphic matroid induced by G, we define the Rayleigh monotonicity of the generating polynomial for the set of bases of a matroid and suggest a few related problems. (C) 2007 Elsevier B.V. All rights reserved.
- Keywords
- Graph; Matroid; Generating polynomial; Rayleigh monotonicity; HALF-PLANE PROPERTY; POLYNOMIALS; THEOREMS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/29195
- DOI
- 10.1016/J.DISC.2007.
- ISSN
- 0012-365X
- Article Type
- Article
- Files in This Item:
- There are no files associated with this item.
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