Wave equations for graphs and the edge-based Laplacian
type: Item
instance of: scholarly article
title: Wave equations for graphs and the edge-based Laplacian
zbMATH Open document ID: 1072.35107
author: Joel Friedman
author: Jean-Pierre Tillich
published in: Pacific Journal of Mathematics
publication date: 2005-02-24T00:00:00Z
review text: The authors study what appears to be a new type of wave equation on graphs. This wave equation (1) involves a reasonable analogue of \(u_{tt}=\Delta u\) in analysis, (2) has ``finite speed of propagation'' and many other basic properties shared by its analysis counterpart, and (3) seems to be a good vehicle for translating results in analysis to those in graph theory, and vice versa. This wave equation requires some of the notions of ``calculus of graphs'' from an unpublished preprint of the authors. As one of the examples, the authors give a simple proof of a relation between distances of sets, their sizes, and the first nonzero edge-based eigenvalue -- which can be better (or worse) than that of [\textit{F. R. K. Chung, V. Faber, T. A. Manteuffel}, SIAM J. Discrete Math. 7 (3), 443--457 (1994; Zbl 0808.05072)].
reviewed by: Dragan Stevanović
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 2138444
zbMATH Keywords: finite speed of propagation
zbMATH Keywords: distances of sets
MaRDI profile type: Publication
full work available at URL: pjm.2004.216.229
OpenAlex ID: W2024489992
DOI: 10.2140/PJM.2004.216.229
description: scientific article; zbMATH DE number 2138444