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A Necessary and Sufficient Condition for the Uniqueness of Minimum Spanning Tree

Maman A. Djauhari

Abstract. We develop a fundamental property of min-max transitive closure of a dissimilarity, considered as a fuzzry relation, in connection with its subdominant ultrametric. This will enable us firstly to derive a necessary and sufficient condition for the uniqueness of its minimum spanning tree, and secondly to find all possible local minima.


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