Generalized Zagreb index of some dendrimer structures

Chemical graph theory, is a branch of mathematical chemistry which deals with the nontrivial applications of graph theory to solve molecular problem. A chemical graph is represent a molecule by considering the atoms as the vertices and bonds between them as the edges. A topological index is a graph based molecular descriptor, which is graph theoretic invariant characterising some physicochemical properties of chemical compounds. Dendrimers are generally large, complex, and hyper branched molecules synthesized by repeatable steps with nanometre scale measurements. In this paper, we study the $(a,b)$-Zagreb index of some regular dendrimers and hence obtain some vertex degree based topological indices.