## Ars Combinatoria, Volumes 11-12Department of Combinatorics and Optimization, University of Waterloo., 1981 - Combinatorial analysis |

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### Contents

We considered potential computational assistance for this problem | 7 |

A Family of Optimal Trees | 37 |

Existence of Orthogonal Diagonal Latin Squares | 51 |

Copyright | |

10 other sections not shown

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### Common terms and phrases

1-factor 1-indecomposable 4-lines abelian group adder adjacent affine array assume automorphism group Baer subplane BIBD bicliques bipartite graph bound cell Combinatorial complete graph connected construction contradiction Corollary cycle cyclic define denote diagonal disjoint elements elliptic semiplane equation example exists finite frame of type frame starter GF(q given graceful graph graceful labeling graph G Graph Theory Hence Howell designs implies incidence structure incident incomplete block designs induced subgraph isomorphic labeling Lemma Let G lines Math matrix modulo O.D.L.S. of order obtained occurs orbits ordered pairs pair of O.D.L.S. pair of orthogonal pairwise parallel class parameters partition perfect matching permutation Petersen graph planar graphs points prime Proof Proposition prove result satisfy solutions square of order square of side Steiner triple systems subdesign subset subsquare of side Suppose symbols symmetric Theorem tree triple systems unique Vanstone vertex vertices