A characterization of bipartite distance-regular graphs

Guang Siang Lee; Chih-wen Weng

doi:10.1016/j.laa.2013.12.024

A characterization of bipartite distance-regular graphs

Guang Siang Lee^*, Chih-wen Weng

^*Corresponding author for this work

Department of Applied Mathematics

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

4 Scopus citations

Abstract

It is well-known that the halved graphs of a bipartite distance-regular graph are distance-regular. Examples are given to show that the converse does not hold. Thus, a natural question is to find out when the converse is true. In this paper we give a quasi-spectral characterization of a connected bipartite weighted 2-punctually distance-regular graph whose halved graphs are distance-regular. In the case the spectral diameter is even we show that the graph characterized above is distance-regular.

Original language	English
Pages (from-to)	91-103
Number of pages	13
Journal	Linear Algebra and Its Applications
Volume	446
DOIs	https://doi.org/10.1016/j.laa.2013.12.024
State	Published - 1 Apr 2014

Keywords

Distance matrices
Distance-regular graph
Predistance polynomials
Spectral diameter
Spectral excess theorem

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abstract = "It is well-known that the halved graphs of a bipartite distance-regular graph are distance-regular. Examples are given to show that the converse does not hold. Thus, a natural question is to find out when the converse is true. In this paper we give a quasi-spectral characterization of a connected bipartite weighted 2-punctually distance-regular graph whose halved graphs are distance-regular. In the case the spectral diameter is even we show that the graph characterized above is distance-regular.",

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AU - Weng, Chih-wen

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AB - It is well-known that the halved graphs of a bipartite distance-regular graph are distance-regular. Examples are given to show that the converse does not hold. Thus, a natural question is to find out when the converse is true. In this paper we give a quasi-spectral characterization of a connected bipartite weighted 2-punctually distance-regular graph whose halved graphs are distance-regular. In the case the spectral diameter is even we show that the graph characterized above is distance-regular.

KW - Distance matrices

KW - Distance-regular graph

KW - Predistance polynomials

KW - Spectral diameter

KW - Spectral excess theorem

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VL - 446

SP - 91

EP - 103

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

A characterization of bipartite distance-regular graphs

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Keywords

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