Graphs whose normalized laplacian has three eigenvalues

E.R. van Dam, G.R. Omidi

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Abstract

We give a combinatorial characterization of graphs whose normalized Laplacian has three distinct eigenvalues. Strongly regular graphs and complete bipartite graphs are examples of such graphs, but we also construct more exotic families of examples from conference graphs, projective planes, and certain quasi-symmetric designs.
Original languageEnglish
Pages (from-to)2560-2569
JournalLinear Algebra and its Applications
Volume435
Issue number10
Publication statusPublished - 2011

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Eigenvalue
Graph in graph theory
Symmetric Design
Strongly Regular Graph
Complete Bipartite Graph
Projective plane
Distinct
Family

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title = "Graphs whose normalized laplacian has three eigenvalues",
abstract = "We give a combinatorial characterization of graphs whose normalized Laplacian has three distinct eigenvalues. Strongly regular graphs and complete bipartite graphs are examples of such graphs, but we also construct more exotic families of examples from conference graphs, projective planes, and certain quasi-symmetric designs.",
author = "{van Dam}, E.R. and G.R. Omidi",
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Graphs whose normalized laplacian has three eigenvalues. / van Dam, E.R.; Omidi, G.R.

In: Linear Algebra and its Applications, Vol. 435, No. 10, 2011, p. 2560-2569.

Research output: Contribution to journalArticleScientificpeer-review

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T1 - Graphs whose normalized laplacian has three eigenvalues

AU - van Dam, E.R.

AU - Omidi, G.R.

PY - 2011

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N2 - We give a combinatorial characterization of graphs whose normalized Laplacian has three distinct eigenvalues. Strongly regular graphs and complete bipartite graphs are examples of such graphs, but we also construct more exotic families of examples from conference graphs, projective planes, and certain quasi-symmetric designs.

AB - We give a combinatorial characterization of graphs whose normalized Laplacian has three distinct eigenvalues. Strongly regular graphs and complete bipartite graphs are examples of such graphs, but we also construct more exotic families of examples from conference graphs, projective planes, and certain quasi-symmetric designs.

M3 - Article

VL - 435

SP - 2560

EP - 2569

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

SN - 0024-3795

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