Distance-regular graphs with diameter 3 and eigenvalue a2 − c3

Quaid Iqbal; Jack H. Koolen; Jongyook Park; Masood Ur Rehman

doi:10.1016/j.laa.2019.10.021

Distance-regular graphs with diameter 3 and eigenvalue a₂ − c₃

Quaid Iqbal
, Jack H. Koolen
, Jongyook Park
, Masood Ur Rehman

University of Science and Technology of China

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

6 Scopus citations

Abstract

In this paper, we consider the distance-regular graphs Γ whose distance-2 graphs Γ₂ are strongly regular. Note that if Γ is bipartite, then its distance-2 graph is not connected. We first show that the distance-2 graph of a non-bipartite distance-regular graph with diameter 3 and eigenvalue a₂−c₃ is strongly regular, and then we give several kinds of classifications of non-bipartite distance-regular graphs with diameter 3 and eigenvalue a₂−c₃.

Original language	English
Pages (from-to)	271-290
Number of pages	20
Journal	Linear Algebra and Its Applications
Volume	587
DOIs	https://doi.org/10.1016/j.laa.2019.10.021
State	Published - 15 Feb 2020

Keywords

Distance-i graphs
Distance-regular graphs
Eigenvalues
Geometric
Strongly regular graphs

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10.1016/j.laa.2019.10.021

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title = "Distance-regular graphs with diameter 3 and eigenvalue a2 − c3 ",

abstract = "In this paper, we consider the distance-regular graphs Γ whose distance-2 graphs Γ2 are strongly regular. Note that if Γ is bipartite, then its distance-2 graph is not connected. We first show that the distance-2 graph of a non-bipartite distance-regular graph with diameter 3 and eigenvalue a2−c3 is strongly regular, and then we give several kinds of classifications of non-bipartite distance-regular graphs with diameter 3 and eigenvalue a2−c3.",

keywords = "Distance-i graphs, Distance-regular graphs, Eigenvalues, Geometric, Strongly regular graphs",

author = "Quaid Iqbal and Koolen, \{Jack H.\} and Jongyook Park and Rehman, \{Masood Ur\}",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2020",

month = feb,

day = "15",

doi = "10.1016/j.laa.2019.10.021",

language = "English",

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journal = "Linear Algebra and Its Applications",

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T1 - Distance-regular graphs with diameter 3 and eigenvalue a2 − c3

AU - Iqbal, Quaid

AU - Koolen, Jack H.

AU - Park, Jongyook

AU - Rehman, Masood Ur

PY - 2020/2/15

Y1 - 2020/2/15

N2 - In this paper, we consider the distance-regular graphs Γ whose distance-2 graphs Γ2 are strongly regular. Note that if Γ is bipartite, then its distance-2 graph is not connected. We first show that the distance-2 graph of a non-bipartite distance-regular graph with diameter 3 and eigenvalue a2−c3 is strongly regular, and then we give several kinds of classifications of non-bipartite distance-regular graphs with diameter 3 and eigenvalue a2−c3.

AB - In this paper, we consider the distance-regular graphs Γ whose distance-2 graphs Γ2 are strongly regular. Note that if Γ is bipartite, then its distance-2 graph is not connected. We first show that the distance-2 graph of a non-bipartite distance-regular graph with diameter 3 and eigenvalue a2−c3 is strongly regular, and then we give several kinds of classifications of non-bipartite distance-regular graphs with diameter 3 and eigenvalue a2−c3.

KW - Distance-i graphs

KW - Distance-regular graphs

KW - Eigenvalues

KW - Geometric

KW - Strongly regular graphs

UR - https://www.scopus.com/pages/publications/85075110854

U2 - 10.1016/j.laa.2019.10.021

DO - 10.1016/j.laa.2019.10.021

M3 - Article

AN - SCOPUS:85075110854

SN - 0024-3795

VL - 587

SP - 271

EP - 290

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Distance-regular graphs with diameter 3 and eigenvalue a₂ − c₃

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Keywords

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Distance-regular graphs with diameter 3 and eigenvalue a2 − c3

Abstract

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Distance-regular graphs with diameter 3 and eigenvalue a₂ − c₃