TY - JOUR

T1 - Computing topological indices of Sudoku graphs

AU - Gao, Wei

AU - Imran, Muhammad

AU - Baig, Abdul Qudair

AU - Ali, Haidar

AU - Farahani, Mohammad Reza

N1 - Funding Information:
This research is supported by COMSATS Attock via grant no. 16-51/CRGP/CIIT/ATK/14/654, by the grant of Higher Education Commission of Pakistan via Ref. No. 20-367/NRPU/R&D/HEC/12/831 and by National University of Sciences and Technology, Islamabad, Pakistan.
Publisher Copyright:
© 2016, Korean Society for Computational and Applied Mathematics.

PY - 2017/10/1

Y1 - 2017/10/1

N2 - 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 Rα(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.

AB - 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 Rα(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.

KW - Atom-bond connectivity (ABC) index

KW - General Randić index

KW - Geometric-arithmetic (GA) index

KW - Sudoku Graph

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U2 - 10.1007/s12190-016-1027-6

DO - 10.1007/s12190-016-1027-6

M3 - Article

AN - SCOPUS:84973610910

SN - 1598-5865

VL - 55

SP - 99

EP - 117

JO - Journal of Applied Mathematics and Computing

JF - Journal of Applied Mathematics and Computing

IS - 1-2

ER -