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Journal of Applied Mathematics and Computing
Published in: Journal of Applied Mathematics and Computing 1-2/2017

09-06-2016 | Original Research

Computing topological indices of Sudoku graphs

Authors: Wei Gao, Muhammad Imran, Abdul Qudair Baig, Haidar Ali, Mohammad Reza Farahani

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2017

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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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Metadata
Title
Computing topological indices of Sudoku graphs
Authors
Wei Gao
Muhammad Imran
Abdul Qudair Baig
Haidar Ali
Mohammad Reza Farahani
Publication date
09-06-2016
Publisher
Springer Berlin Heidelberg
Published in
Journal of Applied Mathematics and Computing / Issue 1-2/2017
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-016-1027-6

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