Identifying structural isomorphism between two kinematic chains via nano topology

Abstract

This research paper aims to analyse the structural equivalence of two undirected graphs via nano topology. Nano homeomorphism has been applied to identify the similarity between two graphs. We have proposed a new notion to define the neighbourhood of a vertex of an undirected graph and have defined the approximations through the neighbourhood and found out the nano topologies induced by the vertices of the graph and discussed the nano homeomorphisms and nano isomorphisms. We have checked the structural equivalence of the graphs via nano isomorphism. Also we have proposed an algorithm and have checked the structural equivalence of two kinematic chains by using nano isomorphism.