On topological properties of hierarchical interconnection networks

Abstract

There is really a lot of mathematics involved in electrical and electronic engineering. It depends on what area of electrical and electronic engineering, for example there is a lot more abstract mathematics in communication theory and signal processing and networking etc. Networks involve nodes communicating with each other. A lot of computers linked together form a network. Cell phone users form a network. Networking involves the study of the best way of implementing a network. Graph theory has found a considerable use in this area of research. In this paper, we extend this study to interconnection networks and derive analytical closed results of general Randic index $$R_{\alpha }(G)$$ for different values of “ $$\alpha $$ ” for block shift network (BSN-1) and (BSN-2), Hierarchical hypercube (HHC-1) and (HHC-2). We also compute first Zagreb, $$\textit{ABC}$$ , $$\textit{GA}$$ , $$\textit{ABC}_{4}$$ and $$\textit{GA}_{5}$$ indices and give closed formulae of these indices for Hierarchical interconnection networks.