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a-stable adjacent alliance number Archimedean and Laves array baselines basic blocks binary tree bond percolation C„XCm-Sk column Combinatorial communication sets complete graph Computer Congressus Numerantium connected consider contains Corollary critical probabilities dd(G defined deleted denote disks dominating set edge labels edge with initial edge-graceful elements endpoints equation exactly exists fc-tuples Figure finite free vertex function Genetic Algorithm graph G Graph Theory Hamiltonian cycle Hamiltonian path heuristic hybrid incident initial vertex intersect isomorphic Latin squares Laves lattices Lemma Let G Math Mathematics monochromatic solution node obtain optimal pair parity path permutation planar graph planar Ramsey numbers plane polygon polyominoes positive integers problem Proof real number representation resp rgood routing s-star sequence of order signed graph Skolem sequence Skolem-graceful strings subgraph subtrees t-extended Table tetrahedron Theorem tilings topology transversals trominoes vertex a-stable vertical edge vertices of degree