DSpace
 

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/10054/6404

Title: Average distance in graphs and eigenvalues
Authors: SIVASUBRAMANIAN, S
Issue Date: 2009
Publisher: ELSEVIER SCIENCE BV
Citation: DISCRETE MATHEMATICS, 309(10), 3458-3462
Abstract: Brendan McKay gave the following formula relating the average distance between pairs of vertices in a tree T and the eigenvalues of its Laplacian: (d) over bar (T) = 2/n-1 Sigma(n)(i=2) 1/lambda(i). By modifying Mohar's proof of this result, we prove that for any graph G, its average distance, (d) over bar (G), between pairs of vertices satisfies the following inequality: (d) over bar (G) >= 2/n-1 Sigma(n)(i=2) 1/lambda(i). This solves a conjecture of Graffiti. We also present a generalization of this result to the average of suitably defined distances for k subsets of a graph. (C) 2008
URI: http://dx.doi.org/10.1016/j.disc.2008.09.044
http://dspace.library.iitb.ac.in/xmlui/handle/10054/6404
http://hdl.handle.net/10054/6404
ISSN: 0012-365X
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