An odd characterization of the generalized odd graphs

E.R. van Dam; W.H. Haemers

doi:10.1016/j.jctb.2011.03.001

An odd characterization of the generalized odd graphs

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Abstract

We show that any connected regular graph with d + 1 distinct eigenvalues and odd-girth 2d + 1 is distance-regular, and in particular that it is a generalized odd graph.

Original language	English
Pages (from-to)	486-489
Journal	Journal of Combinatorial Theory Series B
Volume	101
Issue number	6
DOIs	https://doi.org/10.1016/j.jctb.2011.03.001
Publication status	Published - 2011

Keywords

distance-regular graphs
generalized odd graphs
odd-girth
spectra of graphs
spectral excess theorem
spectral characterization

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10.1016/j.jctb.2011.03.001

Dam1Accepted author manuscript, 123 KB

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title = "An odd characterization of the generalized odd graphs",

abstract = "We show that any connected regular graph with d + 1 distinct eigenvalues and odd-girth 2d + 1 is distance-regular, and in particular that it is a generalized odd graph. ",

keywords = "distance-regular graphs, generalized odd graphs, odd-girth, spectra of graphs, spectral excess theorem, spectral characterization",

author = "\{van Dam\}, E.R. and W.H. Haemers",

note = "Appeared earlier as CentER Discussion Paper 2010-047",

year = "2011",

doi = "10.1016/j.jctb.2011.03.001",

language = "English",

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journal = "Journal of Combinatorial Theory Series B",

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AU - van Dam, E.R.

AU - Haemers, W.H.

N1 - Appeared earlier as CentER Discussion Paper 2010-047

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Y1 - 2011

N2 - We show that any connected regular graph with d + 1 distinct eigenvalues and odd-girth 2d + 1 is distance-regular, and in particular that it is a generalized odd graph.

AB - We show that any connected regular graph with d + 1 distinct eigenvalues and odd-girth 2d + 1 is distance-regular, and in particular that it is a generalized odd graph.

KW - distance-regular graphs

KW - generalized odd graphs

KW - odd-girth

KW - spectra of graphs

KW - spectral excess theorem

KW - spectral characterization

U2 - 10.1016/j.jctb.2011.03.001

DO - 10.1016/j.jctb.2011.03.001

M3 - Article

SN - 0095-8956

VL - 101

SP - 486

EP - 489

JO - Journal of Combinatorial Theory Series B

JF - Journal of Combinatorial Theory Series B

IS - 6

ER -

An odd characterization of the generalized odd graphs

Abstract

Keywords

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