An Unenumerative DNA Computing Model for Vertex Coloring Problem

The solution space exponential explosion caused by the enumeration of the candidate solutions maybe is the biggest obstacle in DNA computing. In the paper, a new unenumerative DNA computing model for graph vertex coloring problem is presented based on two techniques: 1) ordering the vertex sequence for a given graph in such a way that any two consecutive labeled vertices i and i+1 should be adjacent in the graph as much as possible; 2) reducing the number of encodings representing colors according to the construture of the given graph. A graph with 12 vertices without triangles is solved and its initial solution space includes only 283 DNA strands, which is 0.0532 of 3¹² (the worst complexity).