The following is a summary of the irreducible T-modules (ITMs) and corresponding dimensions of the Terwilliger algebra (dim T) for the 13 distance-regular graphs with valency three.
Select a graph to explore its Terwilliger algebra in detail.
Select a graph to explore its Terwilliger algebra in detail.
| Graph Γ | |Γ| | # ITMs | # Types | dim T Formulation | |
|---|---|---|---|---|---|
| K₄ | 4 | 3 | 2 | 22 + 12 = 5 | Explore → |
| K₃,₃ | 6 | 4 | 3 | 32 + 12 + 12 = 11 | Explore → |
| Petersen | 10 | 6 | 4 | 32 + 22 + 12 + 12 = 15 | Explore → |
| 3-cube | 8 | 3 | 2 | 42 + 22 = 20 | Explore → |
| Heawood | 14 | 6 | 3 | 42 + 22 + 22 = 24 | Explore → |
| Pappus | 18 | 7 | 5 | 52 + 32 + 12 + 22 + 22 = 43 | Explore → |
| Tutte's 8-cage | 30 | 13 | 6 | 52 + 32 + 32 + 12 + 22 + 12 = 49 | Explore → |
| Desargues | 20 | 6 | 4 | 62 + 42 + 22 + 22 = 60 | Explore → |
| Coxeter | 28 | 8 | 6 | 52 + 52 + 22 + 42 + 12 + 22 = 75 | Explore → |
| Dodecahedron | 20 | 4 | 3 | 62 + 62 + 22 = 76 | Explore → |
| Tutte's 12-cage | 126 | 37 | 10 | 72 + 4(52) + 32 + 2(22) + 2(12) = 168 | Explore → |
| Foster | 90 | 18 | 9 | 92 + 2(72) + 52 + 3(42) + 22 + 12 = 257 | Explore → |
| Biggs-Smith | 102 | 10 | 5 | 82 + 132 + 112 + 92 + 42 = 451 | Explore → |