Topological properties of cellular neural networks

Graph theory is a fundamental and energetic tool for designing and modeling a graph/network. There are certain topological indices based on degree, distance and eccentricity, etc. The topological indices essentially relate certain physio-concoction properties and bio-activity to the corresponding synthetic and atomic structure. In this paper, our aim is to figure out degree-based topological indices mainly atom-bond connectivity ( ABC ), geometric-arithmetic ( GA ), ABC 4 and GA 5 indices for cellular neural network (CNN) and give closed results of these indices for cellular neural network. Moreover, we also compute general Randi c ´ index R α of CNN for α = { 1 , - 1 , 1 2 , - 1 2 } only and give analytical closed form results. A 3D graph analysis for comparison of indices is also given.