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In this paper a new approximation algorithm for calculating the min-cut tree of an undirected edgeweighted graph has been proposed. This algorithm runs where V is the number of vertices in the given graph and d is the degree of the graph. It is a significant improvement over time complexities of existing solutions. However, because of an assumption it does not produce correct result for all sort of graphs but for the dense graphs success rate is more than 90%. Moreover in the unsuccessfuldoi:10.5120/12864-9693 fatcat:xc3vuka6wfaw3bki7xguc7g6m4