Juanyan Fang, Muhammad Rafiullah and Hafiz Muhammad Afzal Siddiqui*
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.
Topological indices, Molecular descriptors, Zagrib indices, Eccentricity, Sierpinski graphs, Chemical graphs
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