Investigation of the Partition Dimension in Chemical Networks and its Application in Chemistry

Abstract

‎Partition dimension problems involve dividing a graph's vertex set into a minimum number of disjoint sets so that each vertex is different with respect to the representation from each disjoint set‎. ‎As a result of the development of this method‎, ‎a number of applications have arisen in a number of fields such as drug design‎, ‎navigation of robots‎, ‎pattern recognition‎, ‎and image processing‎. ‎In this paper‎, ‎we have calculated the partition dimension of oxide and {zigzag benzenoid networks‎, ‎and the subdivision of benzenoid hydrocarbon and triangular benzene networks.