A Molecular Solution for the Ramsey Number Based on AuNP Self-Assembly
The Ramsey number plays an important role in logic analysis. The complexity of finding a solution for the Ramsey number when the value of the clique pairs is large, becomes greatly high, and the solution space becomes rather large, thus only 9 Ramsey numbers have been found. DNA computing
due to its strong parallelism has made breakthroughs in solving NP complete problem, of which the Ramsey number is part, while traditional computers have been unable to solve it. We provide a new molecular model using a graph transformation model that converts triangles into vertices. In constructing
the physical model, we design a specific recognition vertex based on AuNP self-assembly in order to detect the feasibility of the solution. Finally, an example of a non-solution 4(3, 3) is verified and excluded from the solution space by finding the counterexample of the inverse negative propositions
of the Ramsey theorem.
Keywords: DNA Computing; Gold Nanoparticles; Graph Transformation Model; Ramsey Number; Self-Assembly
Document Type: Research Article
Affiliations: 1: School of Control and Computer Engineering, North China Electric Power University, Beijing, 102206, China 2: Institute of Software, School of Electronics Engineering and Computer Science, Peking University, Beijing, 100871, China
Publication date: 01 July 2016
- Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
- Editorial Board
- Information for Authors
- Submit a Paper
- Subscribe to this Title
- Terms & Conditions
- Ingenta Connect is not responsible for the content or availability of external websites
- Access Key
- Free content
- Partial Free content
- New content
- Open access content
- Partial Open access content
- Subscribed content
- Partial Subscribed content
- Free trial content