scispace - formally typeset
Proceedings ArticleDOI

Clique-Detection Algorithm Using Clique-Self-Assembly

27 Sep 2011-pp 225-230
TL;DR: This work answers the question: Can a given set of graphs be generated through the self-assembly of clique-self-assembly and concludes that the problem of finding the generator is decidable.
Abstract: Self-assembly is a process in which simple objects autonomously combine themselves into larger objects. It is considered as a promising technique in nano-technology. Two simple graphs G1 and G2 with a clique of same size overlap and a new self-assembled graph is formed. Besides studying the properties of self assembled graphs on cliques, we answer the question: Can a given set of graphs be generated through the self-assembly of cliques? If so, how to find the generator that could generate the given set of graphs by the process of clique-self-assembly. The question of the existence of minimal generator is also discussed. The necessary and sufficient condition for a graph H to be obtained by the iterated clique-self-assembly of the graph G is also answered. We also conclude that the problem of finding the generator is decidable. We note the importance of our work with respect to several closely related clique finding problem.
Topics: Clique graph (72%), Clique-sum (72%), Chordal graph (71%), Clique problem (70%), Split graph (69%)
References
More filters

Book
01 Jan 1976-
Abstract: (1977). Graph Theory with Applications. Journal of the Operational Research Society: Vol. 28, Volume 28, issue 1, pp. 237-238.

7,219 citations


Book
01 Jan 1980-
TL;DR: This new Annals edition continues to convey the message that intersection graph models are a necessary and important tool for solving real-world problems and remains a stepping stone from which the reader may embark on one of many fascinating research trails.
Abstract: Algorithmic Graph Theory and Perfect Graphs, first published in 1980, has become the classic introduction to the field. This new Annals edition continues to convey the message that intersection graph models are a necessary and important tool for solving real-world problems. It remains a stepping stone from which the reader may embark on one of many fascinating research trails. The past twenty years have been an amazingly fruitful period of research in algorithmic graph theory and structured families of graphs. Especially important have been the theory and applications of new intersection graph models such as generalizations of permutation graphs and interval graphs. These have lead to new families of perfect graphs and many algorithmic results. These are surveyed in the new Epilogue chapter in this second edition. New edition of the "Classic" book on the topic Wonderful introduction to a rich research area Leading author in the field of algorithmic graph theory Beautifully written for the new mathematician or computer scientist Comprehensive treatment

4,086 citations


Journal ArticleDOI
01 Nov 1994-Science
TL;DR: This experiment demonstrates the feasibility of carrying out computations at the molecular level by solving an instance of the directed Hamiltonian path problem with standard protocols and enzymes.
Abstract: The tools of molecular biology were used to solve an instance of the directed Hamiltonian path problem. A small graph was encoded in molecules of DNA, and the "operations" of the computation were performed with standard protocols and enzymes. This experiment demonstrates the feasibility of carrying out computations at the molecular level.

3,982 citations


Journal ArticleDOI
06 Aug 1998-Nature
TL;DR: The design and observation of two-dimensional crystalline forms of DNA that self-assemble from synthetic DNA double-crossover molecules that create specific periodic patterns on the nanometre scale are reported.
Abstract: Molecular self-assembly presents a `bottom-up' approach to the fabrication of objects specified with nanometre precision. DNA molecular structures and intermolecular interactions are particularly amenable to the design and synthesis of complex molecular objects. We report the design and observation of two-dimensional crystalline forms of DNA that self-assemble from synthetic DNA double-crossover molecules. Intermolecular interactions between the structural units are programmed by the design of `sticky ends' that associate according to Watson-Crick complementarity, enabling us to create specific periodic patterns on the nanometre scale. The patterned crystals have been visualized by atomic force microscopy.

2,542 citations


Journal ArticleDOI
01 Jun 1986-Order

1,233 citations