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abelian group adjacency matrix algorithm ANNE PENFOLD arrangement x,n Australia ABSTRACT Axiom coloured Combinatory Logic complete graph conference matrix conjecture is true construction contains corresponding coset graph crew cycle defining relations denote Department of Mathematics edges elementary operation elements example exists Figure finite following first rows forecasting function given Graph Theory group G Hadamard matrices Hall planes Harary Hence incidence matrix indicator customers integral isomorphic JENNIFER WALLIS k-l k-l k-simplices lattice LEMMA Math matrix of order maximal sum-free set node non-isomorphic obtained occur one-coloured triangles one-factorizations path pay fortnight permutation Phys points polynomial problem PROOF reconstructed regular 2-graph roster S+I S+I satisfying Schreier coset graph self-avoiding semi-stable shifts skew skew-Hadamard matrix solution squares of side standardized Room square strong graph subgraphs subgroup summand Suppose Sykes THEOREM translation plane tree Ulam's conjecture University of Newcastle vertex vertices W.D. WALLIS worker