Distance-regular Cayley graphs with least eigenvalue -2

Edwin van Dam, Alireza Abdollahi, Mojtaba Jazaeri

Research output: Contribution to journalArticleScientificpeer-review

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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 languageEnglish
Pages (from-to)73-85
JournalDesigns, Codes and Cryptography
Volume84
Issue number1-2
DOIs
Publication statusPublished - 2017

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Least Eigenvalue
Distance-regular Graph
Cayley Graph
Graph in graph theory
Line Graph
Incidence
Classify
Generalized Polygon
Projective plane
Triangular

Keywords

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

Cite this

van Dam, Edwin ; Abdollahi, Alireza ; Jazaeri, Mojtaba. / Distance-regular Cayley graphs with least eigenvalue -2. In: Designs, Codes and Cryptography. 2017 ; Vol. 84, No. 1-2. pp. 73-85.
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Distance-regular Cayley graphs with least eigenvalue -2. / van Dam, Edwin; Abdollahi, Alireza; Jazaeri, Mojtaba.

In: Designs, Codes and Cryptography, Vol. 84, No. 1-2, 2017, p. 73-85.

Research output: Contribution to journalArticleScientificpeer-review

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AU - van Dam, Edwin

AU - Abdollahi, Alireza

AU - Jazaeri, Mojtaba

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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

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DO - 10.1007/s10623-016-0209-4

M3 - Article

VL - 84

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EP - 85

JO - Designs, Codes and Cryptography

JF - Designs, Codes and Cryptography

SN - 0925-1022

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