Graphs with integral spectrum

Omran Ahmadi; Noga Alon; Ian F. Blake; Igor E. Shparlinski

doi:10.1016/j.laa.2008.08.020

Graphs with integral spectrum

Omran Ahmadi, Noga Alon, Ian F. Blake, Igor E. Shparlinski

Research output: Contribution to journal › Article › peer-review

70 Scopus citations

Abstract

It is shown that only a fraction of 2^{- Ω (n)} of the graphs on n vertices have an integral spectrum. Although there are several explicit constructions of such graphs, no upper bound for their number has been known. Graphs of this type play an important role in quantum networks supporting the so-called perfect state transfer.

Original language	English (US)
Pages (from-to)	547-552
Number of pages	6
Journal	Linear Algebra and Its Applications
Volume	430
Issue number	1
DOIs	https://doi.org/10.1016/j.laa.2008.08.020
State	Published - Jan 1 2009
Externally published	Yes

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

Keywords

Cayley graph
Graph spectrum
Integral eigenvalue
Random matrix

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10.1016/j.laa.2008.08.020

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title = "Graphs with integral spectrum",

abstract = "It is shown that only a fraction of 2- Ω (n) of the graphs on n vertices have an integral spectrum. Although there are several explicit constructions of such graphs, no upper bound for their number has been known. Graphs of this type play an important role in quantum networks supporting the so-called perfect state transfer.",

keywords = "Cayley graph, Graph spectrum, Integral eigenvalue, Random matrix",

author = "Omran Ahmadi and Noga Alon and Blake, {Ian F.} and Shparlinski, {Igor E.}",

note = "Funding Information: Research of N.A. was supported USA–Israeli BSF grant, by a grant from the Israel Science Foundation, and by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University, that of I.F.B. by NSERC Grant A 7382, and that of I.S. was supported by ARC Grant DP0556431.",

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doi = "10.1016/j.laa.2008.08.020",

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T1 - Graphs with integral spectrum

AU - Ahmadi, Omran

AU - Alon, Noga

AU - Blake, Ian F.

AU - Shparlinski, Igor E.

N1 - Funding Information: Research of N.A. was supported USA–Israeli BSF grant, by a grant from the Israel Science Foundation, and by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University, that of I.F.B. by NSERC Grant A 7382, and that of I.S. was supported by ARC Grant DP0556431.

PY - 2009/1/1

Y1 - 2009/1/1

N2 - It is shown that only a fraction of 2- Ω (n) of the graphs on n vertices have an integral spectrum. Although there are several explicit constructions of such graphs, no upper bound for their number has been known. Graphs of this type play an important role in quantum networks supporting the so-called perfect state transfer.

AB - It is shown that only a fraction of 2- Ω (n) of the graphs on n vertices have an integral spectrum. Although there are several explicit constructions of such graphs, no upper bound for their number has been known. Graphs of this type play an important role in quantum networks supporting the so-called perfect state transfer.

KW - Cayley graph

KW - Graph spectrum

KW - Integral eigenvalue

KW - Random matrix

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DO - 10.1016/j.laa.2008.08.020

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SN - 0024-3795

VL - 430

SP - 547

EP - 552

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1

ER -

Graphs with integral spectrum

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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