<abstract><p>In this work we obtain new lower and upper optimal bounds of general Sombor indices. Specifically, get inequalities for these indices relating them with other indices: the first Zagreb index, forgotten index variable index. Finally, solve some extremal problems indices.</p></abstract>

We show how generalized Zagreb indices $M_1^k(G)$ can be computed by using a simple graph polynomial and Stirling numbers of the second kind. In that way we explain and clarify the meaning of a triangle of numbers used to establish the same result in an earlier reference.

In this paper, we compute the formulae for the third Zagreb indices and its coindices for two classes of graphs such as edge corona product graph, double graph and kth iterated double graph.

There is a natural linkage between the molecular structures and the bio-medical and pharmacology characteristics. A topological index can be considered as transformation of chemical structure in to real number and has been used as a predictor parameter. There are certain vertex-degree-based topological indices which has been used extensively in the chemical graph theory but recently no further ...

Expressions for the Zagreb indices and coindices of the total graph, semi-total point graph and of semi-total line graph of subdivision graphs in terms of the parameters of the parent graph are obtained, thus generalizing earlier existing results.

For any simple connected undirected graph, it is well known that the Kirchhoff and multiplicative degree-Kirchhoff indices can be computed using the Laplacian matrix. We show that the same is true for the additive degree-Kirchhoff index and give a compact Matlab program that computes all three Kirchhoffian indices with the Laplacian matrix as the only input.