Computing topological indices of Sudoku graphs

Abstract

In QSAR/QSPR study, physico-chemical properties and topological indices such as Randic, 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 Randic index $$R_{\alpha }(G)$$ for different values of “ $$\alpha $$ ” for Sudoku (SK). We also compute the general Randic, first Zagreb, ABC, GA, $$ABC_{4}$$ and $$GA_{5}$$ indices and give closed formulae of these indices for Sudoku graphs.