Computing topological indices of Sudoku graphs

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× n Sudoku graphs and derive analytical closed results of general Randić index R_α(G) for different values of for Sudoku (SK). We also compute the general Randić, first Zagreb, ABC, GA, ABC₄ and GA₅ indices and give closed formulae of these indices for Sudoku graphs.