2-Walk-regular graphs with a small number of vertices compared to the valency

Zhi Qiao; Jack H. Koolen; Jongyook Park

doi:10.1016/j.laa.2016.07.027

2-Walk-regular graphs with a small number of vertices compared to the valency

Zhi Qiao
, Jack H. Koolen
, Jongyook Park

Sichuan Normal University
University of Science and Technology of China
Chinese Academy of Sciences

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

3 Scopus citations

Abstract

In 2013, it was shown that, for a given real number α>2, there are only finitely many distance-regular graphs Γ with valency k and diameter D≥3 having at most αk vertices, except for the following two cases: (i) D=3 and Γ is imprimitive; (ii) D=4 and Γ is antipodal and bipartite. In this paper, we will generalize this result to 2-walk-regular graphs. In this case, also incidence graphs of certain group divisible designs appear.

Original language	English
Pages (from-to)	10-24
Number of pages	15
Journal	Linear Algebra and Its Applications
Volume	510
DOIs	https://doi.org/10.1016/j.laa.2016.07.027
State	Published - 1 Dec 2016

Keywords

Distance-regular graphs
Dual property
Group divisible designs
t-walk-regular graphs

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title = "2-Walk-regular graphs with a small number of vertices compared to the valency",

abstract = "In 2013, it was shown that, for a given real number α>2, there are only finitely many distance-regular graphs Γ with valency k and diameter D≥3 having at most αk vertices, except for the following two cases: (i) D=3 and Γ is imprimitive; (ii) D=4 and Γ is antipodal and bipartite. In this paper, we will generalize this result to 2-walk-regular graphs. In this case, also incidence graphs of certain group divisible designs appear.",

keywords = "Distance-regular graphs, Dual property, Group divisible designs, t-walk-regular graphs",

author = "Zhi Qiao and Koolen, \{Jack H.\} and Jongyook Park",

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AU - Qiao, Zhi

AU - Koolen, Jack H.

AU - Park, Jongyook

PY - 2016/12/1

Y1 - 2016/12/1

N2 - In 2013, it was shown that, for a given real number α>2, there are only finitely many distance-regular graphs Γ with valency k and diameter D≥3 having at most αk vertices, except for the following two cases: (i) D=3 and Γ is imprimitive; (ii) D=4 and Γ is antipodal and bipartite. In this paper, we will generalize this result to 2-walk-regular graphs. In this case, also incidence graphs of certain group divisible designs appear.

AB - In 2013, it was shown that, for a given real number α>2, there are only finitely many distance-regular graphs Γ with valency k and diameter D≥3 having at most αk vertices, except for the following two cases: (i) D=3 and Γ is imprimitive; (ii) D=4 and Γ is antipodal and bipartite. In this paper, we will generalize this result to 2-walk-regular graphs. In this case, also incidence graphs of certain group divisible designs appear.

KW - Distance-regular graphs

KW - Dual property

KW - Group divisible designs

KW - t-walk-regular graphs

UR - https://www.scopus.com/pages/publications/84982126104

U2 - 10.1016/j.laa.2016.07.027

DO - 10.1016/j.laa.2016.07.027

M3 - Article

AN - SCOPUS:84982126104

SN - 0024-3795

VL - 510

SP - 10

EP - 24

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

2-Walk-regular graphs with a small number of vertices compared to the valency

Abstract

Keywords

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