TY - JOUR
T1 - On topological indices of certain interconnection networks
AU - Imran, Muhammad
AU - Hayat, Sakander
AU - Mailk, Muhammad Yasir Hayat
N1 - Funding Information:
This research is supported by National University of Sciences and Technology (NUST), Islamabad and Higher Education Commission of Pakistan via Grant No. 20-367/NRPU/R&D/HEC/12/831 .
PY - 2014/10/1
Y1 - 2014/10/1
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 properties of certain networks are studied recently in [13] by Hayat and Imran (2014). In this paper, we extend this study to interconnection networks and derive analytical closed results of general Randić index Rα(G) for different values of "α" for butterfly and Benes networks. We also compute first Zagreb, ABC, and GA indices for these important classes of networks. Moreover, we construct two new classes of mesh derived networks by using some basic operations of graphs on m×n mesh networks, and then study certain topological indices for these classes of networks.
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 properties of certain networks are studied recently in [13] by Hayat and Imran (2014). In this paper, we extend this study to interconnection networks and derive analytical closed results of general Randić index Rα(G) for different values of "α" for butterfly and Benes networks. We also compute first Zagreb, ABC, and GA indices for these important classes of networks. Moreover, we construct two new classes of mesh derived networks by using some basic operations of graphs on m×n mesh networks, and then study certain topological indices for these classes of networks.
KW - Atom-bond connectivity (ABC) index
KW - Benes network
KW - Butterfly network
KW - General Randić index
KW - Geometric-arithmetic (GA) index
KW - Mesh derived network
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U2 - 10.1016/j.amc.2014.07.064
DO - 10.1016/j.amc.2014.07.064
M3 - Article
AN - SCOPUS:84907317006
SN - 0096-3003
VL - 244
SP - 936
EP - 951
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
ER -