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Title:  qAnalogs of distance matrices of 3hypertrees 
Authors:  SIVASUBRAMANIAN, S 
Keywords:  theorem tree 
Issue Date:  2009 
Publisher:  ELSEVIER SCIENCE INC 
Citation:  LINEAR ALGEBRA AND ITS APPLICATIONS, 431(8), 12341248 
Abstract:  We consider the distance matrix of trees in 3uniform hypergraphs (which we call 3hypertrees). We give a formula for the inverse of a few qanalogs of distance matrices of 3hypertrees 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 3hypertree T depends only on n, the number of vertices of T. Further, we give a Pfaffian identity for a principal submatrix of some (skewsymmetrized) distance matrices of 3hypertrees 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 2connected 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 http://dspace.library.iitb.ac.in/xmlui/handle/10054/7206 http://hdl.handle.net/10054/7206 
ISSN:  00243795 
Appears in Collections:  Article

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