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Three-helix structure of the DNA molecule provided by the emergence of a new type of computing model, it has high stability, low rate of wrong solutions, easy separation and so on. Especially during the reaction data pool and the final solution was to come in the form of double-stranded, so avoid the hairpin structure, greatly improved the correct rate of solution. Minimum spanning tree problem is a NP-difficult problems in graph theory, which is looking for the tree contains all vertices and the smallest right of an undirected graph. We will attempt using of triplex DNA computing model for this article to solve the minimum spanning tree problem in graph theory.

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