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The dominating set concept in graphs has been used in many applications. In large graphs finding the minimum dominating set is difficult. The minimum dominating set problem in graphs seek a set D of minimum number of vertices such that each vertex of the graph is either in D or adjacent to a vertex in D. In a graph on n nodes if there is a single node of degree n-1 then that single node forms a minimum dominating set. In the proposed paper, a designed network called Graph Neural Network (GNN) is used to identify the node of degree N-1 in a graph having a single node of degree N-1 as it forms the minimum dominating set in the graph.
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