Clique-Detection Algorithm Using Clique-Self-Assembly

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.