Let F be a distance-regular graph with valency k (k >I 2) and diameter at least 2, and denote by ;t 1 and 2%~m the second largest and least eigenvalue of F, respectively. Assume the multiplicity m( )O of some eigenvalue ;~ ( )~ :/: k) of F satisfies m( Z ) < k. Then ;~ = Z 1 or )'rot. and either (i)
A new condition for distance-regular graphs
β Scribed by J.H. Koolen
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 109 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Given a nontrivial primitive idempotent E of a distance-regular graph/-with diameter d ~> 3, we obtain an inequality involving the intersection numbers of F for each integer i (3 ~< i ~< d). We show equality is attained for i = 3 if and only if equality is attained for all i (3 ~< i ~< d) if and onl
Let β« be a distance-regular graph with l (1 , a 1 , b 1 ) Ο 1 and c s Ο© 1 Ο 1 for some positive integer s . We show the existence of a certain distance-regular graph of diameter s , containing given two vertices at distance s , as a subgraph in β« .
Let β« be a distance-regular graph with a 1 ΟΎ 0 , r Ο max Ν j 3 ( c j , a j , b j ) Ο ( c 1 , a 1 , b 1 ) Ν Ρ 2 and a i Ο a 1 c i , for 1 Ρ i Ρ 2 r . Take any u and in β« at distance r Ο© 1 . We show that there exists a collinearity graph of a generalized 2( r Ο© 1)-gon of order ( a 1 Ο© 1 , c r Ο© 1 Οͺ 1)