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/100/18386

Title: THE SECOND IMMANANT OF SOME COMBINATORIAL MATRICES
Authors: BAPAT, RB
SIVASUBRAMANIAN, S
Keywords: PRODUCT DISTANCE MATRIX
TREE
GRAPH
Issue Date: 2015
Publisher: UNIV ISFAHAN, VICE PRESIDENT RESEARCH & TECHNOLOGY
Citation: TRANSACTIONS ON COMBINATORICS, 4(2)23-35
Abstract: Let A = (a(i,j))(1 <= i,j <= n) be an n x n matrix where n >= 2. Let det2(A), its second immanant be the immanant corresponding to the partition lambda(2) = 2,1(n-2) Let G be a connected graph with blocks B-1, B-2, . . . . B-p and with q-exponential distance matrix EDG. We give an explicit formula for det2(EDG) which shows that det2(EDG) is independent of the manner in which G's blocks are connected. Our result is similar in form to the result of Graham, Hoffman and Hosoya and in spirit to that of Bapat, Lal and Pati who show that det EDT where T is a tree is independent of the structure of T and only dependent on its number of vertices. Our result extends more generally to a product distance matrix associated to a connected graph G. Similar results are shown for the q-analogue of T's laplacian and a suitably defined matrix for arbitrary connected graphs.
URI: http://dspace.library.iitb.ac.in/jspui/handle/100/18386
ISSN: 2251-8657
2251-8665
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