Distance-Regular Graphs of Classical Parameters (d, q, a, b)

• Click the “Evaluate” button below to calculate parameters.
• The outputs will be at the bottom.
• Edit the parameters in "array" at the top of the code, and see the results.
• The program below only works for numeric values.
• If you want to get the text form of matrices, edit 'show' to 'print'
• You can get latex-format output as shown below.

• Link to SageCell Server
• Instruction to make similar pages

Examples of Distance-Regular Graphs of Classical Parameters

1. Johnson graph J(n,d): (d, 1, 1, n-d)
2. Grassmann graph J_q(n,d): (d, q, q, q[n-d]_q)
3. Dual polar graph (e = 0, 1/2, 1, 3/2, 2): (d,q,0,q^e)
4. Dual polar graph U(2d,r): (d, -r, r(r+1)/(1-r), (r-(-r)^d+1)/(1-r))
5. Half dual polar graph: D_n.n(q): (d, q², q²+q, q[m]_q), [m=n=2d+1, or m+1 = n = 2d]
6. Exceptional Lie graph E_7,7(q): (3, q⁴, (q³+q²+q+1)q, q[9]_q)
7. Gosset graph E₇(1): (3, 1, 4, 9)
8. Triality graph ³D_4,2(q): (3, -q, q/(1-q), q(q+1))
9. Witt graph M₂₄: (3, -2, -4, 10)
10. Witt graph M₂₃: (3, -2, -2, 5)
11. Hamming graph H(d,n): (d, 1, 0, n-1)
12. Halved cube (1/2)H(n,2): (d,1,2,m), [m=n=2d+1, or m+1 = n = 2d]
13. Bilinear forms graph: (d, q, q-1, qⁿ-1)
14. Alternating forms graph: (d, q², q²-1, q^m-1), [m=n=2d+1, or m+1 = n = 2d]
15. Heamitean forms graph q = r²: (d, -r, -r-1, -(-r)^d-1)
16. Affine E₆(q) graph: (3, q⁴, q⁴-1, q⁹-1)
17. Extended ternary Golay code graph: (3, -2, -3, 8)
18. Pseudo D_m(q) graphs: (d, q, 0, 1)
19. Dist. 1-or-2 in symplectic dual polar graph: (d, q², q(q+1), q[m]_q)
20. Doob graph: (d, 1, 0, 3)
21. Quadratic forms graph: (d, q², q²-1, q^m-1), , [m=n=2d-1, or m-1 = n = 2d]