Classical Distance-Regular Graphs of Negative Type

Chih-wen Weng

doi:10.1006/jctb.1998.1892

Classical Distance-Regular Graphs of Negative Type

Chih-wen Weng^*

^*Corresponding author for this work

Department of Applied Mathematics

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

35 Scopus citations

Abstract

We prove the following theorem. \emsp;Theorem.Let Γ=(X, R)denote a distance-regular graph with classical parameters(d, b, α, β)and d≥4.Suppose b<-1,and suppose the intersection numbers a₁≠0,c₂>1.Then precisely one of the following(i)-(iii)holds. (i)Γ is the dual polar graph²A_2d-1(-b). (ii)Γ is the Hermitian forms graph Her_-b(d). (iii)α=(b-1)/2,β=-(1+b^d)/2,and-b is a power of an odd prime.

Original language	English
Pages (from-to)	93-116
Number of pages	24
Journal	Journal of Combinatorial Theory. Series B
Volume	76
Issue number	1
DOIs	https://doi.org/10.1006/jctb.1998.1892
State	Published - May 1999

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title = "Classical Distance-Regular Graphs of Negative Type",

abstract = "We prove the following theorem. \textbackslash{}emsp;Theorem.Let Γ=(X, R)denote a distance-regular graph with classical parameters(d, b, α, β)and d≥4.Suppose b<-1,and suppose the intersection numbers a1≠0,c2>1.Then precisely one of the following(i)-(iii)holds. (i)Γ is the dual polar graph2A2d-1(-b). (ii)Γ is the Hermitian forms graph Her-b(d). (iii)α=(b-1)/2,β=-(1+bd)/2,and-b is a power of an odd prime.",

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N2 - We prove the following theorem. \emsp;Theorem.Let Γ=(X, R)denote a distance-regular graph with classical parameters(d, b, α, β)and d≥4.Suppose b<-1,and suppose the intersection numbers a1≠0,c2>1.Then precisely one of the following(i)-(iii)holds. (i)Γ is the dual polar graph2A2d-1(-b). (ii)Γ is the Hermitian forms graph Her-b(d). (iii)α=(b-1)/2,β=-(1+bd)/2,and-b is a power of an odd prime.

AB - We prove the following theorem. \emsp;Theorem.Let Γ=(X, R)denote a distance-regular graph with classical parameters(d, b, α, β)and d≥4.Suppose b<-1,and suppose the intersection numbers a1≠0,c2>1.Then precisely one of the following(i)-(iii)holds. (i)Γ is the dual polar graph2A2d-1(-b). (ii)Γ is the Hermitian forms graph Her-b(d). (iii)α=(b-1)/2,β=-(1+bd)/2,and-b is a power of an odd prime.

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Classical Distance-Regular Graphs of Negative Type

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