DSpace at IIT Bombay >
IITB Publications >
Article >

Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/jspui/handle/10054/7206

Title: q-Analogs of distance matrices of 3-hypertrees
Keywords: theorem
Issue Date: 2009
Citation: LINEAR ALGEBRA AND ITS APPLICATIONS, 431(8), 1234-1248
Abstract: We consider the distance matrix of trees in 3-uniform hypergraphs (which we call 3-hypertrees). We give a formula for the inverse of a few q-analogs of distance matrices of 3-hypertrees T. Some results are analogs of results by Bapat et al. for graphs. We give an alternate proof of the result that the determinant of the distance matrix of a 3-hypertree T depends only on n, the number of vertices of T. Further, we give a Pfaffian identity for a principal submatrix of some (skew-symmetrized) distance matrices of 3-hypertrees when we fix an ordering of the vertices and assign signs appropriately. A result of Graham, Hoffman and Hosoya relates the determinant of the distance matrix of a graph and the determinants of its 2-connected blocks. When the graph has as blocks a fixed connected graph H which satisfy some conditions, we give a formula for the inverse of its distance matrix. This result generalises a result of Graham and Lovasz. When each block of G is a fixed graph G, we also give some corollaries about the sum of the entries of the inverse of the distance matrix of G and some of its analogs. (C) 2009
URI: http://dx.doi.org/10.1016/j.laa.2009.04.020
ISSN: 0024-3795
Appears in Collections:Article

Files in This Item:

There are no files associated with this item.

View Statistics

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.


Valid XHTML 1.0! DSpace Software Copyright © 2002-2010  Duraspace - Feedback