Vol. 13, No. 3, 2020

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17, 1 issue

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Author Index
Coming Soon
Other MSP Journals
A Cheeger inequality for graphs based on a reflection principle

Edward Gelernt, Diana Halikias, Charles Kenney and Nicholas F. Marshall

Vol. 13 (2020), No. 3, 475–486

Given a graph with a designated set of boundary vertices, we define a new notion of a Neumann Laplace operator on a graph using a reflection principle. We show that the first eigenvalue of this Neumann graph Laplacian satisfies a Cheeger inequality.

Cheeger inequality, graph Laplacian, Neumann Laplacian
Mathematical Subject Classification 2010
Primary: 05C50, 05C85
Secondary: 15A42
Received: 4 December 2019
Revised: 9 May 2020
Accepted: 23 May 2020
Published: 14 July 2020

Communicated by Glenn Hurlbert
Edward Gelernt
Department of Mathematics
Yale University
New Haven, CT
United States
Diana Halikias
Department of Mathematics
Yale University
New Haven, CT
United States
Charles Kenney
Department of Mathematics
Rutgers University
Piscataway, NJ
United States
Nicholas F. Marshall
Department of Mathematics
Princeton University
Princeton, NJ
United States