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Distance regular subgraphs of a cube

✍ Scribed by Paul M. Weichsel

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
826 KB
Volume
109
Category
Article
ISSN
0012-365X

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πŸ“œ SIMILAR VOLUMES

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We classify distance-regular graphs that are isometrically embeddable into halved cube graphs.

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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)

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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 )