We provide a combinatorial description of all the minors of the edge version of the Laplacian matrix of a mixed tree. The description involves the common SDR's for the forests obtained by deleting from the tree the edge sets corresponding to the row and column indices of the minor.
Description
Edge version of the matrix tree theorem for trees: Linear and Multilinear Algebra: Vol 47, No 3
%0 Journal Article
%1 ravindra00
%A Bapat, Ravindra B.
%A Grossman, Jerrold W.
%A Kulkarni, Devadatta M.
%D 2000
%J Linear and Multilinear Algebra
%K eigenvalues graph.theory matrix matrix.tree.theorem
%N 3
%P 217--229
%R 10.1080/03081080008818646
%T Edge version of the matrix tree theorem for trees
%V 47
%X We provide a combinatorial description of all the minors of the edge version of the Laplacian matrix of a mixed tree. The description involves the common SDR's for the forests obtained by deleting from the tree the edge sets corresponding to the row and column indices of the minor.
@article{ravindra00,
abstract = { We provide a combinatorial description of all the minors of the edge version of the Laplacian matrix of a mixed tree. The description involves the common SDR's for the forests obtained by deleting from the tree the edge sets corresponding to the row and column indices of the minor. },
added-at = {2017-01-19T12:47:57.000+0100},
author = {Bapat, Ravindra B. and Grossman, Jerrold W. and Kulkarni, Devadatta M.},
biburl = {https://www.bibsonomy.org/bibtex/2eb041866d7ece3450aaa8ce5c0581868/ytyoun},
description = {Edge version of the matrix tree theorem for trees: Linear and Multilinear Algebra: Vol 47, No 3},
doi = {10.1080/03081080008818646},
interhash = {d2e0d4007171e04f0363c9f1e71aea12},
intrahash = {eb041866d7ece3450aaa8ce5c0581868},
journal = {Linear and Multilinear Algebra},
keywords = {eigenvalues graph.theory matrix matrix.tree.theorem},
number = 3,
pages = {217--229},
timestamp = {2017-02-01T04:30:01.000+0100},
title = {Edge version of the matrix tree theorem for trees},
volume = 47,
year = 2000
}