A parallel type of DNA computing model for graph vertex coloring problem

A DNA computing model for solving graph vertex coloring problem is proposed in this article. To illustrate the capability of the DNA computing model, a 3-colorable graph with 61 vertices was constructed as an example. Using this model, more than 99% of false solutions were deleted when the initial solution space was established and finally all solutions of the graph were found. Because these operations can be used for any graph with 61 vertices, the searching capability of this model could be up to O(3⁵⁹). This searching capability is the largest among both electronic and non-electronic computers after the DNA computing model (with searching capability of O(2²⁰) ) proposed by Adleman´s research group in 2002.