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 -