Icosahedron designs

It is known from the work of Adams and Bryant that icosahedron designs of order v exist for v ≡ 1 (mod 60) as well as for v = 16. Here we prove that icosahedron designs exist if and only if v ≡ 1, 16, 21 or 36 (mod 60), wit

Designs for graphs with six vertices and nine edges

The design spectrum has been determined for eleven of the 21 graphs with six vertices and nine edges. In this paper we completely solve the design spectrum problem for the remaining ten graphs

Completing the design spectra for graphs with six vertices and eight edges

Apart from two possible exceptions, the design spectrum has been determined for every graph with six vertices and at most eight edges. The purpose of this note is to establish the existence of the two missing designs, both of order 32

Theta Graph Designs

We solve the design spectrum problem for all theta graphs with 10, 11, 12, 13, 14 and 15 edges