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Topological properties of Sierpinski network and its application

Author(s):

Juanyan Fang, Muhammad Rafiullah and Hafiz Muhammad Afzal Siddiqui*  

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 that 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, physicochemical properties of chemical structures, 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, Molecular descriptors, Zagrib indices, Eccentricity, Sierpinski graphs, Chemical graphs

Affiliation:

Institute of Mathematics and Computer Science, Tongling College, Tongling 244000, Department of Mathematics, COMSATS University Islamabad, Lahore Campus, 54000, Department of Mathematics, COMSATS University Islamabad, Lahore Campus, 54000



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