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09-06-2016 | Original Research | Issue 1-2/2017

Journal of Applied Mathematics and Computing 1-2/2017

Computing topological indices of Sudoku graphs

Journal:
Journal of Applied Mathematics and Computing > Issue 1-2/2017
Authors:
Wei Gao, Muhammad Imran, Abdul Qudair Baig, Haidar Ali, Mohammad Reza Farahani

Abstract

In QSAR/QSPR study, physico-chemical properties and topological indices such as Randić, atom-bond connectivity (ABC) and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. A topological index is actually designed by transforming a chemical structure into a numeric number. These topological indices correlate certain physico-chemical properties like boiling point, stability, strain energy etc. of chemical compounds. Graph theory has found a considerable use in this area of research. The topological indices of certain interconnection networks were studied recently by Imran et al. (Appl Math Comput 244:936–951, 2014). In this paper, we extend this study to \(n\times n\) Sudoku graphs and derive analytical closed results of general Randić index \(R_{\alpha }(G)\) for different values of “\(\alpha \)” for Sudoku (SK). We also compute the general Randić, first Zagreb, ABC, GA, \(ABC_{4}\) and \(GA_{5}\) indices and give closed formulae of these indices for Sudoku graphs.

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