Weighted graph Laplacians and isoperimetric inequalities

F.R.K. Chung and Kevin Oden

Vol. 192 (2000), No. 2, 257–273

DOI: 10.2140/pjm.2000.192.257

Abstract

We consider a weighted Cheeger’s constant for a graph and we examine the gap between the first two eigenvalues of Laplacian. We establish several isoperimetric inequalities concerning the unweighted Cheeger’s constant, weighted Cheeger’s constants and eigenvalues for Neumann and Dirichlet conditions.

Milestones

Received: 12 June 1996

Revised: 30 April 1998

Published: 1 February 2000