✦ LIBER ✦

Distance-regularised graphs are distance-regular or distance-biregular

✍ Scribed by Chris D Godsil; John Shawe-Taylor

Publisher: Elsevier Science
Year: 1987
Tongue: English
Weight: 506 KB
Volume: 43
Category: Article
ISSN: 0095-8956
DOI: 10.1016/0095-8956(87)90027-x

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

Distance-biregular graphs with 2-valent

Distance-biregular graphs with 2-valent vertices and distance-regular line graphs

✍ Bojan Mohar; John Shawe-Taylor 📂 Article 📅 1985 🏛 Elsevier Science 🌐 English ⚖ 525 KB

Distance Biregular Bipartite Graphs

✍ C. Delorme 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 392 KB

We describe here some properties of a class of graphs which extends the class of distance regular graphs: our graphs are bipartite and for cach vertex there exists an intersection array depending on the stable component of the vertex. Thus our graphs arc to distance regular graphs as bipartite regul

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 ⌫ .

Distance-regular Subgraphs in a Distance

Distance-regular Subgraphs in a Distance-regular Graph, IV

✍ 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, V

✍ A. Hiraki 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 186 KB

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 )