Strongly Regular Graph Database

▸ Companion page: automorphisms of order 3 — known graphs recovered, open parameters mapped

Feasible parameter sets for SRGs with 178 entries (v ≤ 100), cross-checked against the authoritative table of A.E. Brouwer — Parameters of strongly regular graphs (v≤50, 51≤v≤100, retrieved 2026-05-30). Rows in purple are parameters where this project constructed new graphs this session — each independently verified as a valid SRG with the stated automorphism order. Status legend: exists a graph is known · open existence undecided · ∄ proven non-existent. “+” = exists, many graphs, full set not classified.

178

Parameter sets

121

Exist

Open existence

Non-existent

Exist, unclassified (+)

Params we extended

2,697,379

New graphs we added

All Exist Open Non-existent Unclassified (+) Our new graphs

v	k	λ	μ	r^f / s^g	status	#known	#new (ours)	Sage DB	comments / constructions

Provenance & cross-check. Parameter list, eigenvalues, existence status and known counts are taken verbatim from Brouwer's tables (retrieved 2026-05-30) and re-rendered here; the original HTML is archived under data/ for audit. The #new (ours) column counts graphs constructed in this project this session by an Ihringer-style Godsil–McKay switching cascade from low-symmetry de Caen seeds, each verified independently as a valid SRG (degree, λ, μ) with automorphism order computed by dreadnaut. These parameters are Brouwer-“+” (exist, not fully classified); our graphs are asymmetric (|Aut| not divisible by 6), hence outside every published prescribed-automorphism enumeration. Method and caveats: docs/new_srgs_2026_05_30.md. Second cross-check — SageMath. The Sage DB column is the verdict of sage.graphs.strongly_regular_graph(v,k,λ,μ, existence=True) (Cohen–Pasechnik's programmatic implementation of Brouwer's tables): “✓ builds” = Sage constructs a representative, “?” = existence unknown to Sage, “∄” = Sage proves non-existence. For our three parameters Sage independently confirms existence, and every sampled graph of ours was re-verified by Sage's is_strongly_regular() and found non-isomorphic to Sage's representative (see scripts/sage_srg_crosscheck.sage). This page is a static snapshot — regenerate with python3 srg-database/build.py.