Graph designs for eight graphs with six vertices and eight edges (index >1)

{A, B, C, D}. H1 : (A, 3, 1, 0, 6, B), (A, 7, 5, 4, 2, B), (B, 7, 3, C, 6, 5), (D, 3, 7, C, 2, 6), (4, 6, D, 1, 3, A), (B, 4, 2, 1, 7, D), (6, 0, B, 3, 5, A), (0, 4, B, 3, D, 5), (3, 5, C, 0, 2, A), (B, 2, 6, C, 1, D), (C, 1, 7, 6, 4, A), (4, 0, A, 7, D, 6), (1, 5, C, 4, A, 6), (D, 2, 0, 7, 5, B), (A, 1, 5, B, 0, C). H3 : (A, 7, 5, 4, 2, B), (3, 7, B, 6, C, 2), (1, 3, A, 6, 0, 5), (B, 2, 6, C, 1, A), (D, 6, 4, 3, 1, A), (C, 1, 7, 6, 4, D), (4, 0, A, 7, D, 2), (0, 2, D, 5, 7, 6), (C, 5, 3, 2, 0, A), (B, 0, 6, 5, 3, 2), (A, 1, 5, B, 0, 6), (7, 3, D, 2, C, 5), (2, 4, B, 7, 1, 6), (C, 5, 1, A, 4, D), (B, 4, 0, D, 3, C). D1 : (6, 7, D, 0, 3, A), (2, 3, A, 4, 7, B), (1, 7, A, 0, C, 6), (5, 3, B, 4, C, 7), (1, 5, A, 6, 4, C), (3, 1, A, 2, B, 0), (3, 4, B, 5, 0, C), (2, 0, D, 1, A, 6), (D, 4, A, 5, 6, 0), (5, 6,D, 7, 2, B), (0, 1, C, 2, 5, D), (B, 5, C, 6, 7, 0), (4, 0, B, 1, 7, A), (4, 2, C, 3, D, 1), (1, 2, D, 3, 6, B). D3 : (1, 3, C, 2, 5, 0), (6, 0, 3, 4, D, A), (3, 5, 0, 4, B, 1), (2, B, 6, A, 0, C), (0, 2, 6, 3, D, B), Research supported by NSFC Grant 10671055 and NSFHB Grant A2007000230 E-mail: yld6@163.com Corresponding author: qdkang@heinfo.net.