## Combinatorial mathematics III: proceedings of the third Australian conference held at the University of Queensland, 16-18 May, 1974 |

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6-star decomposable 8Z 6Z oe Abelian group algorithm Anne Penfold automorphism average path length Baumert-Hall arrays chromial circuits complete graph component consider construction contains a transposition Corollary D. A. Holton decomposition denote Department of Mathematics derivation tree designs difference elations elements exist F G H finite fixed follows G2 is stable Gj o G2 graph G Hadamard matrices Hall planes Hall system Hence incidence matrix index-0 graph isomorphic Jennifer Seberry left-right path Lemma Math maximal set modulo Moore graphs nodes non-terminal non-zero notation obtain one-factors orbits orthogonal partial stabilising sequence permutation graph players Proof q-star qk+j qk+j+1 result right hand side Roman numeral rule satisfied semi-stable shortest terminal string shown in Figure stability index subgroups subset sum-free sets Suppose T-matrices Theory tournaments tt tt University of Queensland valency vertex W. T. Tutte Wallis zero