Topological Properties of Sierpinski Network and its Application

Abstract

Background: Sierpinski graphs S(n, k) are largely studied because of their fractal nature with applications in topology, chemistry, mathematics of Tower of Hanoi and computer sciences. Applications of molecular structure descriptors are a standard procedure which are used to correlate the biological activity of molecules with their chemical structures, and thus can be helpful in the field of pharmacology.

Objective: The aim of this article is to establish analytically closed computing formulae for eccentricity-based descriptors of Sierpinski networks and their regularizations. These computing formulae are useful to determine a large number of properties like thermodynamic properties, physicochemical properties, chemical and biological activity of chemical graphs Methods: At first, vertex sets have been partitioned on the basis of their degrees, eccentricities and frequencies of occurrence. Then these partitions are used to compute the eccentricity-based indices with the aid of some combinatorics.

Results: The total eccentric index and eccentric-connectivity index have been computed. We also compute some eccentricity-based Zagreb indices of the Sierpinski networks. Moreover, a comparison has also been presented in the form of graphs.

Conclusion: These computations will help the readers to estimate the thermodynamic properties and physicochemical properties of chemical structure which are of fractal nature and can not be dealt with easily. A 3D graphical representation is also presented to understand the dynamics of the aforementioned topological descriptors.

Keywords: Topological indices; Zagrib indices; chemical graphs.; eccentricity; molecular descriptors; sierpinski graphs.