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Distance-regular subgraphs in a distance-regular graph, II

✍ Scribed by Akira Hiraki

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
585 KB
Volume
16
Category
Article
ISSN
0195-6698

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πŸ“œ SIMILAR VOLUMES

Distance-regular Subgraphs in a Distance
Distance-regular Subgraphs in a Distance-regular Graph, III
✍ Akira Hiraki πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 254 KB

Let ⌫ be a distance-regular graph with l (1 , a 1 , b 1 ) ϭ 1 and c s ϩ 1 ϭ 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 ⌫ .

Distance-regular Subgraphs in a Distance
Distance-regular Subgraphs in a Distance-regular Graph, IV
✍ Akira Hiraki πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 280 KB

Let ⌫ 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– Ρƒ 2 and a i Ο­ a 1 c i , for 1 Ρ€ i Ρ€ 2 r . Take any u and in ⌫ 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)

Distance-regular Subgraphs in a Distance
Distance-regular Subgraphs in a Distance-regular Graph, VI
✍ A. Hiraki πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 202 KB

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 )