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The Girth of a Directed Distance-Regular Graph

✍ Scribed by D.A. Leonard; K. Nomura


Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
149 KB
Volume
58
Category
Article
ISSN
0095-8956

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πŸ“œ SIMILAR VOLUMES


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 )

On the distance matrix of a directed gra
✍ R. L. Graham; A. J. Hoffman; H. Hosoya πŸ“‚ Article πŸ“… 1977 πŸ› John Wiley and Sons 🌐 English βš– 144 KB πŸ‘ 2 views

## Abstract In this note, we show how the determinant of the distance matrix __D(G__) of a weighted, directed graph __G__ can be explicitly expressed in terms of the corresponding determinants for the (strong) blocks __G~i~__ of __G__. In particular, when cof __D(G__), the sum of the cofactors of _

The Local Structure of a Bipartite Dista
✍ Brian Curtin πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 285 KB

In this paper, we consider a bipartite distance-regular graph = (X, E) with diameter d β‰₯ 3. We investigate the local structure of , focusing on those vertices with distance at most 2 from a given vertex x. To do this, we consider a subalgebra R = R(x) of Mat X (C), where X denotes the set of vertice