Zagreb Connection Numbers for Cellular Neural Networks

Abstract

Neural networks in which communication works only among the neighboring units are called cellular neural networks (CNNs). These are used in analyzing 3D surfaces, image processing, modeling biological vision, and reducing nonvisual problems of geometric maps and sensory-motor organs. Topological indices (TIs) are mathematical models of the (molecular) networks or structures which are presented in the form of numerical values, constitutional formulas, or numerical functions. These models predict the various chemical or structural properties of the under-study networks. We now consider analogous graph invariants, based on the second connection number of vertices, called Zagreb connection indices. The main objective of this paper is to compute these connection indices for the cellular neural networks (CNNs). In order to find their efficiency, a comparison among the obtained indices of CNN is also performed in the form of numerical tables and 3D plots.