%0 Journal Article %1 choe08 %A Choe, YoungBin %D 2008 %J Discrete Mathematics %K combinatorics graph.theory matroid monotonicity rayleigh %N 24 %P 5944--5953 %R 10.1016/j.disc.2007.11.011 %T A Combinatorial Proof of the Rayleigh Formula for Graphs %V 308 %X 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.

@article{choe08, 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. }, added-at = {2016-06-07T11:32:54.000+0200}, author = {Choe, YoungBin}, biburl = {https://www.bibsonomy.org/bibtex/2d5e63b667bd502ef686d4545cac03e33/ytyoun}, doi = {10.1016/j.disc.2007.11.011}, interhash = {4b5dcacc1dfd2c3123f7d7caaf700906}, intrahash = {d5e63b667bd502ef686d4545cac03e33}, issn = {0012-365X}, journal = {Discrete Mathematics }, keywords = {combinatorics graph.theory matroid monotonicity rayleigh}, number = 24, pages = {5944--5953}, timestamp = {2016-06-07T11:37:53.000+0200}, title = {A Combinatorial Proof of the {Rayleigh} Formula for Graphs }, volume = 308, year = 2008 }