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.