A distance-transitive antipodal cover of a complete graph K n possesses an automorphism group that acts 2-transitively on the fibres. The classification of finite simple groups implies a classification of finite 2-transitive permutation groups, and this allows us to determine all possibilities for s
Antipodal covering graphs
β Scribed by A Gardiner
- Publisher
- Elsevier Science
- Year
- 1974
- Tongue
- English
- Weight
- 937 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
This paper completes the classification of antipodal distance-transitive covers of the complete bipartite graphs K k , k , where k Ρ 3 . For such a cover the antipodal blocks must have size r Ρ k . Although the case r Ο k has already been considered , we give a unified treatment of r Ρ k . We use d
The antipodal graph of a graph G, denoted by A(G), is the graph on the same vertices as of G, two vertices being adjacent if the distance between them is equal to the diameter of G. A graph is said to be antipodal if it is the antipodal graph A (I4) of some graph H. We give a necessary and sufficien
Let 1 be a distance-regular graph of diameter d and valency k>2. If b t =1 and 2t d, then 1 is an antipodal double-cover. Consequently, if f >2 is the multiplicity of an eigenvalue of the adjacency matrix of 1 and if 1 is not an antipodal doublecover then d 2f&3. This result is an improvement of God
We show that a distance-regular graph of valency k ΟΎ 2 is antipodal , if b 2 Ο 1 . This answers Problem (i) on p . 182 of Brouwer , Cohen and Neumaier [4] .
A graph is antipodal if, for every vertex c', there exists exactly one vertex V which is not closer to r than every vertex adjacent to 6. In this paper we consider the problem of characterizing tope graphs of oriented matroids, which constitute a broad class of antipodal graphs. One of the results i