A \(q\)-analogue of Graham, Hoffman and Hosoya's theorem
type: Item
instance of: scholarly article
title: A \(q\)-analogue of Graham, Hoffman and Hosoya's theorem
zbMATH Open document ID: 1188.05027
author: Sivaramakrishnan Sivasubramanian
published in: The Electronic Journal of Combinatorics
publication date: 2010-06-16T00:00:00Z
full work available at URL: https://eudml.org/doc/230532
full work available at URL: v17i1n21.html
review text: Summary: \textit{R.L. Graham}, \textit{A.J. Hoffman}, and \textit{H. Hosoya} [``On the distance matrix of a directed graph'', J. Graph Theory 1, 85--88 (1977; Zbl 0363.05034)] gave a very nice formula about the determinant of the distance matrix \(D_G\) of a graph \(G\) in terms of the distance matrix of its blocks. We generalize this result to a \(q\)-analogue of \(D_G\). Our generalization yields results about the equality of the determinant of the mod-2 (and in general mod-\(k\)) distance matrix (i.e. each entry of the distance matrix is taken modulo 2 or \(k\)) of some graphs. The mod-2 case can be interpreted as a determinant equality result for the adjacency matrix of some graphs.
Mathematics Subject Classification ID: 05A30
Mathematics Subject Classification ID: 05C12
zbMATH DE Number: 5721430
zbMATH Keywords: determinant
zbMATH Keywords: distance matrix
zbMATH Keywords: q-analogue
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5721430