The First and Second Zagreb Index of Complement Graph and Its Applications of Molecular Graph

Abstract

In this paper, some basic mathematical operation for the second Zagreb indices of graph containing the join and strong product of graph operation, and the rst and second Zagreb indices of complement graph operations such as cartesian product G1 G2, composition G1 G2, disjunction G1 _ G2, symmetric dierence G1 G2, join G1 + G2, tensor product G1 G2, and strong product G1 G2 will be explained. The results are applied to molecular graph of nanotorus and titania nanotubes.