A study of cellular neural networks with vertex-edge topological descriptors

The Cellular Neural Network (CNN) has various parallel processing applications, image processing, non-linear processing, geometric maps, high-speed computations. It is an analog paradigm, consists of an array of cells that are interconnected locally. Cells can be arranged in different configurations. Each cell has an input, a state, and an output. The cellular neural network allows cells to communicate with the neighbor cells only. It can be represented graphically; cells will represent by vertices and their interconnections will represent by edges. In chemical graph theory, topological descriptors are used to study graph structure and their biological activities. It is a single value that characterizes the whole graph. In this article, the vertex-edge topological descriptors have been calculated for cellular neural network. Results can be used for cellular neural network of any size. This will enhance the applications of cellular neural network in image processing, solving partial differential equations, analyzing 3D surfaces, sensory-motor organs, and modeling biological vision.