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adjacent algorithm Anne Penfold Applications binary bipartite graph Bulletin Combinatorics complete graph conference connected graph consider construction cordial labeling decomposition defined Definition denote diameter distance dominating elements example exists expander coefficient expander graphs Figure finite function geometry given graph G Graph Theory graphical code Hamiltonian cycle Hamiltonian path Hence Institute of Combinatorics integers interval colouring isomorphic Kirkman Medals knight's tours Latin Squares lattice Lemma length Let G locally maximal major subgraphs matching Math matrix minimum mod 3qp Moore graph multiple coverings node number of edges obtained odd degree pattern one-factorization optimal Orthogonal outer face pairs paper parameters Petersen graph planar graph polynomial problem Professor Proof R.G. Stanton result sequence Six End spanning tree Spetses Stedman Triples subgraph of G subsets Terry Griggs Theorem triangle Twin Bob University Upper valid randomization set vertex Vertex Egyptian vertex set weight xyzx Z-cyclic