TY - JOUR
T1 - Classical Distance-Regular Graphs of Negative Type
AU - Weng, Chih-wen
PY - 1999/5/1
Y1 - 1999/5/1
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.
UR - http://www.scopus.com/inward/record.url?scp=0346340978&partnerID=8YFLogxK
U2 - 10.1006/jctb.1998.1892
DO - 10.1006/jctb.1998.1892
M3 - Article
AN - SCOPUS:0346340978
VL - 76
SP - 93
EP - 116
JO - Journal of Combinatorial Theory. Series B
JF - Journal of Combinatorial Theory. Series B
SN - 0095-8956
IS - 1
ER -