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7-labeling adjacent algorithm alphabet graphs Anne Penfold block cells codes colored combinatorial Combinatorial Designs complete graph conference conjecture connected graph construction contains Corollary decomposition defined denote Department of Mathematics diam(G diameter digraph Discrete Math disjoint DP-graph e)-design eccentric digraph elements Euler Medal example exists Fibonacci finite GF(q graph G graph of order Graph Theory grid graphs Hamilton cycles hamiltonian hypergraph induced subgraph Institute of Combinatorics integer isomorphic Kirkman Medals knight's tour labeling of G Leech trees Lemma Let G linear hypergraph matrices metamorphosis obtain odd number orthogonal labelling pair parallel classes path pattern in Figure perfect partition permutation permutation matrices planar polynomial poset positive integer problem Proof radio labeling radio number Ramseian referee result rn(c rn(G Room square Ruet d'Auteuil self-dual codes sequence smallest spanning 2-connected subgraph stable set sub-board subsets Theorem tournament triple systems University vertex set weight