Let Ξ be a regular graph with n vertices, diameter D, and d + 1 In a previous paper, the authors showed that if P (Ξ») > n -1, then D β€ d -1, where P is the polynomial of degree d-1 which takes alternating values Β±1 at Ξ» 1 , . . . , Ξ» d . The graphs satisfying P (Ξ») = n -1, called boundary graphs, h
Retracing Argument for Distance-Regular Graphs
β Scribed by Akira Hiraki
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 220 KB
- Volume
- 79
- Category
- Article
- ISSN
- 0095-8956
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β¦ Synopsis
We introduce the retracing argument for distance-regular graphs and prove several results by applying this argument.
π SIMILAR VOLUMES
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)
In this paper we give a sufficient condition for the existence of a strongly closed subgraph which is (c q + a q )-regular of diameter q containing a given pair of vertices at distance q in a distance-regular graph. Moreover we show that a distance-regular graph with r = max{ j | (c j , a j , b j )