On the Hyper Zagreb Indices of the Subdivision Related Composite Graphs

Abstract

Complex network structures are developed from basic graphs by using the graphical operations. The topological indices serves a crucial part for the prediction of any molecular compound in terms of toxicity of any chemical and the utility of the same for the pharmaceutical and the therapeutic industry. To understand the topology of a molecule, one needs to convert the information contained in a molecule to a numerical value which is when the topological indices comes into picture. In this article, we determine the explicit expressions of the first and second hyper Zagreb indices by the method of combinatorial inequalities for the corona products of the subdivision related graphs notably the subdivision vertex, subdivision edge, subdivision neighborbood vertex, subdivision neighborhood edge and subdivision double corona product of graphs. These graphical operations will facilitate in understanding the underlying topologies of certain complex network graphs.