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A distance regular graph of typeE1°Ed

✍ Scribed by Suogang Gao; Hong You

Publisher
Springer
Year
2000
Tongue
English
Weight
166 KB
Volume
45
Category
Article
ISSN
1001-6538

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📜 SIMILAR VOLUMES

Distance-regular Subgraphs in a Distance
Distance-regular Subgraphs in a Distance-regular Graph, III
✍ Akira Hiraki 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 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 ⌫ .

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✍ Akira Hiraki 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 280 KB

Let ⌫ be a distance-regular graph with a 1 Ͼ 0 , r ϭ max ͕ j 3 ( c j , a j , b j ) ϭ ( c 1 , a 1 , b 1 ) ͖ у 2 and a i ϭ a 1 c i , for 1 р i р 2 r . Take any u and in ⌫ at distance r ϩ 1 . We show that there exists a collinearity graph of a generalized 2( r ϩ 1)-gon of order ( a 1 ϩ 1 , c r ϩ 1 Ϫ 1)

Distance-regular Subgraphs in a Distance
Distance-regular Subgraphs in a Distance-regular Graph, VI
✍ A. Hiraki 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 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 )