A Novel DNA-Based Parallel Computation for Solving Graph Coloring Problems

This study provided molecular solutions for the graph coloring problems (GCP) by two steps: (1) translating vertices to strands and (2) generating DNA procedures. At the first step, we defined strands to present the vertices of graph; on the second step, we applied DNA parallel approach to construct algorithms. DNA computation takes use DNA molecules and biological operations to solve problems in a solution of DNA, where specific combination of DNA is interpreted as a particular result to a problem encoded by molecular. Based on the bio-operation proposed by Adleman and Amos, the proposed approach solves the 3-coloring and k-coloring problems with potential time complexity of O(nXk
²
), where n and k denote the number of vertices of graph G and the smallest positive number to color G, respectively.