Abstract
We introduce the notion of a t-graph and prove that regular 3-graphs are equivalent to cyclic antipodal 3-fold covers of a complete graph. This generalizes the equivalence of regular two-graphs and Taylor graphs. As a consequence, an equivalence between cyclic antipodal distance regular graphs of diameter 3 and certain rank 6 commutative association schemes is proved. New examples of regular 3-graphs are presented.
| Original language | English |
|---|---|
| Pages (from-to) | 99-115 |
| Number of pages | 17 |
| Journal | Ars Mathematica Contemporanea |
| Volume | 6 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2013 |
Keywords
- Antipodal graph
- Association scheme
- Distance regular graph of diameter 3
- Godsil-Hensel matrix
- Group ring
- Taylor graph
- Two-graph
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Algebra and Number Theory
- Geometry and Topology
- Discrete Mathematics and Combinatorics