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adjacent algorithm antimagic labeling ar(G assume auxiliary points Cahit chromatic number clique codes coloring combinatorial complete bipartite graphs complete graph Conjecture connected graph construction contains contradiction Corollary cubic graph defined denote detour dominating disjoint dominating set domination number edge weights embedding exactly exists follows given graph G graph of order Graph Theory Hadamard matrices Hamiltonian cycle Hamming distance Hamming distance distribution Hence idempotent implies induced inequivalent Hadamard matrices isomorphic Lemma Let G line of length magic squares matrices of order maximal independent set minimum obtain orthogonal design packed with 6-cycles pair parallel classes partial cube partition of V(G path planar point of degree positive integers Proposition prove pseudosurface resolving acyclic number resolving acyclic partition resolving partition result semigroup sequence subgraph subset Suppose symmetric difference symmetric Hamming distance Theorem 1.1 tree triangles triples vertex set vertex-transitive graph vertices of G well-covered zero