Distance-regular subgraphs in a distance-regular graph, I
نویسندگان
چکیده
منابع مشابه
Subgraphs Graph in a Distance-regular Graph
Let Γ denote a D-bounded distance-regular graph, where D ≥ 3 is the diameter of Γ. For 0 ≤ s ≤ D − 3 and a weak-geodetically closed subgraph ∆ of Γ with diameter s, define a graph G(∆) whose vertex set is the collection of all weak-geodetically closed subgraphs of diameter s+2 containing ∆, and vertex Ω is adjacent to vertex Ω′ in G if and only if Ω∩Ω′ as a subgraph of Γ has diameter s+1. We sh...
متن کاملA Distance-Regular Graph with Strongly Closed Subgraphs
Let be a distance-regular graph of diameter d, valency k and r := max{i | (ci , bi ) = (c1, b1)}. Let q be an integer with r + 1 ≤ q ≤ d − 1. In this paper we prove the following results: Theorem 1 Suppose for any pair of vertices at distance q there exists a strongly closed subgraph of diameter q containing them. Then for any integer i with 1 ≤ i ≤ q and for any pair of vertices at distance i ...
متن کاملA distance-regular graph with bipartite geodetically closed subgraphs
Let Γ be a distance-regular graph of diameter d , and t be an integer with 2 ≤ t ≤ d − 1 such that at−1 = 0. For any pair (u, v) of vertices, let Π (u, v) be the subgraph induced by the vertices lying on shortest paths between u and v. We prove that if Π (u, v) is a bipartite geodetically closed subgraph for some pair (u, v) of vertices at distance t , then Π (x, y) is a bipartite geodetically ...
متن کاملA Questionable Distance-Regular Graph
In this paper, we introduce distance-regular graphs and develop the intersection algebra for these graphs which is based upon its intersection numbers. We discuss results following from the definition of the intersection algebra. We investigate two examples of distance-regular graphs and show how these results apply. Finally, we introduce parameters that determine intersection numbers. We inves...
متن کاملOn Subgraphs in Distance-Regular Graphs
Terwilliger [15] has given the diameter bound d < (s 1)(k 1) + 1 for distance-regular graphs with girth 2s and valency k. We show that the only distance-regular graphs with even girth which reach this bound are the hypercubes and the doubled Odd graphs. Also we improve this bound for bipartite distance-regular graphs. Weichsel [17] conjectures that the only distance-regular subgraphs of a hyper...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1995
ISSN: 0195-6698
DOI: 10.1016/0195-6698(95)90040-3