Vol. 13, No. 3, 2020

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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
Abstract

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.

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

Communicated by Glenn Hurlbert
Authors
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