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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
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Abstract |
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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. |
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Keywords
Cheeger inequality, graph Laplacian, Neumann Laplacian
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Mathematical Subject Classification 2010
Primary: 05C50, 05C85
Secondary: 15A42
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Milestones
Received: 4 December 2019
Revised: 9 May 2020
Accepted: 23 May 2020
Published: 14 July 2020
Communicated by Glenn Hurlbert
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Authors |
| Edward Gelernt | |
| Department of Mathematics Yale University New Haven, CT United States |
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| Diana Halikias | |
| Department of Mathematics Yale University New Haven, CT United States |
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| Charles Kenney | |
| Department of Mathematics Rutgers University Piscataway, NJ United States |
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| Nicholas F. Marshall | |
| Department of Mathematics Princeton University Princeton, NJ United States |
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