On properties of cell matrices
type: Item
instance of: scholarly article
title: On properties of cell matrices
zbMATH Open document ID: 1203.15022
author: Gašper Jaklič
author: Jolanda Modic
published in: Applied Mathematics and Computation
publication date: 2010-06-25T00:00:00Z
review text: The paper deals with some special classes of matrices, coming from star graphs (or claw graphs) used in graph theory and in biochemistry. A cell matrix \(D=(d_{ij})\) is associated with a vector \((\alpha _{i})\), where \( d_{ii}=0\) and \(d_{ij}=\alpha _{i}+\alpha _{j}\) for \(i\neq j\). Connecting \(k\) star graphs by inner vertices, one obtains a \(k\)-star graph. A Euclidean distance matrix (EDM) is a square \(n\) matrix having as entries the square distance of distances of \(n\) Euclidian points. A circum-Euclidean distance matrix (CEDM) imposes that the Euclidian points lie on a hypersphere. The authors prove that all cell matrices are (C)EDM, but only some special \(k\)-cell matrices are (C)EDM matrices. Some other interesting formulas concerning the calculus of a determinant of a symbolic matrix with polynomial entries are also proved.
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 5726769
zbMATH Keywords: cell matrix
zbMATH Keywords: star graph
zbMATH Keywords: determinant
zbMATH Keywords: eigenvalues
zbMATH Keywords: Euclidean distance matrix
zbMATH Keywords: circum-Euclidean distance matrix
zbMATH Keywords: symbolic matrix
MaRDI profile type: Publication
full work available at URL: j.amc.2010.03.032
OpenAlex ID: W2064406784
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DOI: 10.1016/J.AMC.2010.03.032
description: scientific article; zbMATH DE number 5726769