$\text{Suetake graph }\cong\text{ Incidence graph of } \mathrm{STD}_4[12;3]$

There is a unique symmetric transversal design $\mathrm{STD}_4[12;3]$, as shown by C. Suetake (Designs, Codes and Cryptography 37 (2005), 293–304). Therefore, we introduce the name "Suetake graph" to refer to its incidence graph.

Number of vertices:$72$
Intersection array:$\{12,11,8,1;1,4,11,12\}$
Spectrum:$12^1 (2\sqrt{3})^{24} 0^{22} (-2\sqrt{3})^{24} (-12)^1$
Automorphism group:$\text{Has order }2^6\cdot 3^3=1728$
Bipartite, Antipodal


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Last updated: 7 June 2017