Distance-regular Cayley graphs with least eigenvalue -2

Edwin R. van Dam; Alireza Abdollahi; Mojtaba Jazaeri

doi:10.1007/s10623-016-0209-4

Distance-regular Cayley graphs with least eigenvalue -2

Edwin R. van Dam, Alireza Abdollahi, Mojtaba Jazaeri

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Abstract

We classify the distance-regular Cayley graphs with least eigenvalue −2 and diameter at most three. Besides sporadic examples, these comprise of the lattice graphs, certain triangular graphs, and line graphs of incidence graphs of certain projective planes. In addition, we classify the possible connection sets for the lattice graphs and obtain some results on the structure of distance-regular Cayley line graphs of incidence graphs of generalized polygons.

Original language	English
Pages (from-to)	73-85
Journal	Designs Codes and Cryptography
Volume	84
Issue number	1-2
DOIs	https://doi.org/10.1007/s10623-016-0209-4
Publication status	Published - 2017

Keywords

Cayley graph
strongly regular graph
distance-regular graph
line graph
generalized polygon
eigenvalues

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10.1007/s10623-016-0209-4

Distance-regular Cayley graphsFinal published version, 442 KB

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title = "Distance-regular Cayley graphs with least eigenvalue -2",

abstract = "We classify the distance-regular Cayley graphs with least eigenvalue −2 and diameter at most three. Besides sporadic examples, these comprise of the lattice graphs, certain triangular graphs, and line graphs of incidence graphs of certain projective planes. In addition, we classify the possible connection sets for the lattice graphs and obtain some results on the structure of distance-regular Cayley line graphs of incidence graphs of generalized polygons.",

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author = "{van Dam}, {Edwin R.} and Alireza Abdollahi and Mojtaba Jazaeri",

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T1 - Distance-regular Cayley graphs with least eigenvalue -2

AU - van Dam, Edwin R.

AU - Abdollahi, Alireza

AU - Jazaeri, Mojtaba

PY - 2017

Y1 - 2017

N2 - We classify the distance-regular Cayley graphs with least eigenvalue −2 and diameter at most three. Besides sporadic examples, these comprise of the lattice graphs, certain triangular graphs, and line graphs of incidence graphs of certain projective planes. In addition, we classify the possible connection sets for the lattice graphs and obtain some results on the structure of distance-regular Cayley line graphs of incidence graphs of generalized polygons.

AB - We classify the distance-regular Cayley graphs with least eigenvalue −2 and diameter at most three. Besides sporadic examples, these comprise of the lattice graphs, certain triangular graphs, and line graphs of incidence graphs of certain projective planes. In addition, we classify the possible connection sets for the lattice graphs and obtain some results on the structure of distance-regular Cayley line graphs of incidence graphs of generalized polygons.

KW - Cayley graph

KW - strongly regular graph

KW - distance-regular graph

KW - line graph

KW - generalized polygon

KW - eigenvalues

U2 - 10.1007/s10623-016-0209-4

DO - 10.1007/s10623-016-0209-4

M3 - Article

SN - 0925-1022

VL - 84

SP - 73

EP - 85

JO - Designs Codes and Cryptography

JF - Designs Codes and Cryptography

IS - 1-2

ER -

Distance-regular Cayley graphs with least eigenvalue -2

Abstract

Keywords

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