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adjacent algorithm Anne Penfold Applications broom chromatic number circ clique Colbourn colored Combinatorics complete graphs Computer Science conference conjecture connected graph construction copy Corollary cubic graph cycle decomposition define denote Department of Mathematics digraphs Discrete Mathematics disjoint domination number edges exists a Z-cyclic F-coloring Figure finite Frank Harary G contains graph G graph of order Graph Theory H-cordial Hadamard Hamiltonian Institute of Combinatorics intersection graph Kirkman Medal labeling of G latin squares Lemma length Let G linear magic constant Maiorana-McFarland function Math matrix matroids minimum Note number of walks obtained og(G open geodominating set orthogonal design pair Paley graph partition path Petersen graphs polynomial problem Proof radio labeling Ramsey numbers regular graphs rn(c rn(G Seberry sequence Steiner triple systems subgraph tetrasticks Theorem tournaments tree University upper vertex labels vertex-magic total labeling weight distribution