Antipodal covers of strongly regular graphs
✍ Scribed by Aleksandar Jurišić
- Book ID
- 108316171
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 729 KB
- Volume
- 182
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
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 Ͼ 2 is antipodal , if b 2 ϭ 1 . This answers Problem (i) on p . 182 of Brouwer , Cohen and Neumaier [4] .
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
Let Γ be a regular graph with n vertices, diameter D, and d + 1 In a previous paper, the authors showed that if P (λ) > n -1, then D ≤ d -1, where P is the polynomial of degree d-1 which takes alternating values ±1 at λ 1 , . . . , λ d . The graphs satisfying P (λ) = n -1, called boundary graphs, h