Graph theory provides powerful and efficient tools for the topological characterization of the underline structure. Any problem that contains a graph structure can be analysed and determined by using a graph-theoretical method which in turn extend the scope of applications in different fields of engineering and science. In particular, chemical graph theory addresses the characterization of the underlying topology by offering excellent descriptors that are associated with the structural, and they have the talent to correspond with the observed properties. It is usually brought into service to achieve the quantitative characterization of material structures, thereby empowering the study of quantitative structure toxicity (QSTR), property (QSPR) and activity (QSAR) relationships of the molecular structures.ÂăIn this paper, the different versions of Szeged, Padmakar-Iven (PI) and Mostar indices for the molecular graphs of two types of dendrimers having phthalocyanines and porphyrins as their cores are illustrated through the numerical way.

In this paper, the characterization of closed and strongly closed subobjects of an object in category of semiuniform convergence spaces is given and it is shown that they induce a notion of closure which enjoy the basic properties like idempotency,(weak) hereditariness, and productivity in the category of semiuniform convergence spaces. Furthermore, T1 semiuniform convergence spaces with respect to these two new closure operators are characterized.

In this paper, we present a new generalization of the Perov fixed point theorem on vector-valued metric space. Moreover, to show the significance of our result, we present both a nontrivial comparative example and an application to a kind of semilinear operator system about the existence of its solution.