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Topological indices, i.e., numerical invariants suitably associated to graphs and only depending upon their isomorphism type, have important applications in Chemistry. Their computation constitutes an important branch of Chemical Graph Theory. In this paper, we focus on some degree and distance-based invariants related to the Zagreb indices, the Szeged index and the Wiener index, namely, the F-index, the vertex PI index and the hyper-Wiener index. In particular, we find the formulæ to compute these topological invariants for wreath product of graphs. [ABSTRACT FROM AUTHOR]

The first Zagreb index of a graph G is the sum of squares of the degrees of the vertices of G. In this paper, we introduce generalized four new sums of graphs and study the first Zagreb index and coindex of the resulting graphs. In addition, we give the short proof for the earlier results of Deng, Sarala, Ayyaswamy and Balachandran [Appl. Math. Comput. 275 (2016) 422–431] on the first Zagreb index of four operations on graphs by different approach. [ABSTRACT FROM AUTHOR]