Incidence graphs

Symmetric designs: projective spaces

Heawood graph $\cong$ Incidence graph of $PG(2,2)$
Incidence graph of $PG(2,3)$
Incidence graph of $PG(2,4)$
Incidence graph of $PG(2,5)$
Incidence graph of $PG(2,7)$
Incidence graph of $PG(2,8)$
Incidence graph of $PG(2,9)$
Incidence graph of $PG(2,11)$
Incidence graph of $PG(3,2)$
Incidence graph of $PG(3,3)$
Incidence graph of $PG(4,2)$

Symmetric designs: biplanes

Distance-3 graph of Heawood graph $\cong$ Incidence graph of biplane on 7 points
Incidence graph of biplane on 11 points
Incidence graphs of biplanes on 16 points

Symmetric designs: Hadamard designs

Heawood graph $\cong$ Incidence graph of Hadamard $(7,3,1)$-design
Incidence graph of Hadamard $(11,5,2)$-design
Incidence graphs of Hadamard $(15,7,3)$-designs (3 graphs)
Incidence graphs of Hadamard $(19,9,4)$-designs (6 graphs)

Other symmetric designs

Incidence graph of $(11,6,3)$-design
Incidence graph of $(13,9,3)$-design
Incidence graph of complement of $PG(3,2)$
Incidence graphs of $(15,8,4)$-designs (N=4)
Incidence graphs of $(16,10,6)$-designs
Incidence graph of Higman's symmetric design
Incidence graph of Leonard semibiplanes

Symmetric transversal designs: affine planes minus a parallel class, i.e. $\mathrm{STD}_1[q;q]$

Incidence graph of $AG(2,3)$ minus a parallel class $\cong$ Pappus graph
Incidence graph of $AG(2,4)$ minus a parallel class
Incidence graph of $AG(2,5)$ minus a parallel class
Incidence graph of $AG(2,7)$ minus a parallel class
Incidence graph of $AG(2,8)$ minus a parallel class
Incidence graph of $AG(2,9)$ minus a parallel class

Symmetric transversal designs: $\mathrm{STD}_\lambda[2\lambda;2]$, i.e. Hadamard graphs

Hadamard graph on 16 vertices $\cong$ 4-cube $\cong$ Incidence graph of $\mathrm{STD}_2[4;2]$
Hadamard graph on 32 vertices $\cong$ Incidence graph of $\mathrm{STD}_4[8;2]$
Hadamard graph on 48 vertices $\cong$ Incidence graph of $\mathrm{STD}_6[12;2]$

Other symmetric transversal designs

Hexacode graph $\cong$ Incidence graph of $\mathrm{STD}_2[6;3]$
Incidence graph of $\mathrm{STD}_2[8;4]$
Incidence graph of $\mathrm{STD}_3[9;3]$
Suetake graph $\cong$ Incidence graph of $\mathrm{STD}_4[12;3]$

Generalized polygons

Incidence graph of $GH(2,2) \cong$ Tutte's 12-cage
Incidence graph of $GH(3,3)$
Incidence graph of $GQ(3,3)$
Incidence graph of $GQ(4,4)$

Back to: A-Z index • Graphs by family
Last updated: 7 June 2017