𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Retracing Argument for Distance-Regular Graphs

✍ Scribed by Akira Hiraki


Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
220 KB
Volume
79
Category
Article
ISSN
0095-8956

No coin nor oath required. For personal study only.

✦ Synopsis


We introduce the retracing argument for distance-regular graphs and prove several results by applying this argument.


πŸ“œ SIMILAR VOLUMES


From regular boundary graphs to antipoda
✍ Fiol, M. A.; Garriga, E.; Yebra, J. L. A. πŸ“‚ Article πŸ“… 1998 πŸ› John Wiley and Sons 🌐 English βš– 383 KB πŸ‘ 2 views

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 ≀ 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

Distance-regular Subgraphs in a Distance
✍ 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
✍ 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
✍ 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 )