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THE PRODUCT DISTANCE MATRIX OF A TREE AND A BIVARIATE ZETA FUNCTION OF A GRAPH

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Title THE PRODUCT DISTANCE MATRIX OF A TREE AND A BIVARIATE ZETA FUNCTION OF A GRAPH
 
Creator BAPAT, RB
SIVASUBRAMANIAN, S
 
Subject Laplacian
Ihara-Selberg zeta function
Trees
 
Description In this paper, the product distance matrix of a tree is defined and formulas for its determinant and inverse are obtained. The results generalize known formulas for the exponential distance matrix. When the number of variables are restricted to two, the bivariate analogue of the laplacian matrix of an arbitrary graph is defined. Also defined in this paper is a bivariate analogue of the Ihara-Selberg zeta function and its connection with the bivariate laplacian is shown. Finally, for connected graphs, there is a result connecting a partial derivative of the determinant of the bivariate laplacian and its number of spanning trees.
 
Publisher INT LINEAR ALGEBRA SOC
 
Date 2014-10-17T05:07:24Z
2014-10-17T05:07:24Z
2012
 
Type Article
 
Identifier ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 23275-286
http://dspace.library.iitb.ac.in/jspui/handle/100/16026
 
Language en