Edge version of the matrix tree theorem for trees

Bapat, Ravindra B. ; Grossman, Jerrold W. ; Kulkarni, Devadatta M. (2000) Edge version of the matrix tree theorem for trees Linear and Multilinear Algebra, 47 (3). pp. 217-229. ISSN 0308-1087

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Related URL: http://dx.doi.org/10.1080/03081080008818646


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.

Item Type:Article
Source:Copyright of this article belongs to Taylor and Francis Ltd.
Keywords:Matrix Tree Theorem; Laplacian Matrix; Mixed Graph; Tree; Nonsingular Substructure; System of Distinct Representatives; AMS Subject Classifications (1991): Primary: 05C50; Secondary: 05C05; 15A15
ID Code:1412
Deposited On:05 Oct 2010 12:29
Last Modified:13 May 2011 08:09

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