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A Family of Optimal Trees
Existence of Orthogonal Diagonal Latin Squares
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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