Strongly regular graph srg(n,k,λ,μ): k-regular, adjacent vertices have λ common neighbors, non-adjacent have μ. Parameters must satisfy: k(k-λ-1)=μ(n-k-1). Eigenvalues: k, r, s with multiplicities 1, f, g.
How to Use
Enter parameters:
- (n,k,λ,μ): SRG params
- Eigenvalues: k, r, s
- Feasibility: Check conditions
Famous SRGs
Petersen: srg(10,3,0,1). Paley(q): srg(q,(q-1)/2,(q-5)/4,(q-1)/4) for prime power q≡1(4). Kneser K(5,2): srg(10,3,0,1)=Petersen. Clebsch: srg(16,5,0,2). Schläfli: srg(27,16,10,8).
Feasibility Conditions
Necessary: k(k-λ-1)=μ(n-k-1). Eigenvalues r,s = (λ-μ ± √((λ-μ)²+4(k-μ)))/2 must give integer multiplicities f,g where f+g=n-1. The Krein conditions and absolute bound further restrict parameters.
Step-by-Step Instructions
- 1Enter n,k,λ,μ.
- 2Check feasibility.
- 3Compute eigenvalues.
- 4Find multiplicities.
- 5Identify graph.