On computation of some distance-based topological indices of circulant networks

Year 2018, Volume: 47 Issue: 6, 1427 - 1437, 12.12.2018

Faisal Ali , Abdul Hafeez Muhammad Salman Shuliang Huang

https://izlik.org/JA28JX36XP

Abstract

The distance, $d(u,v)$, between two vertices $u$ and $v$ of a connected graph $G$ is the length of a $u-v$ geodesic in $G$. A large number of graph-distance-based topological indices in various families of graphs and networks have been computed. In this paper, we consider circulant networks and compute three distance-based topological indices, namely the Wiener index, hyper-Wiener index and Schultz molecular topological index on these networks.

Keywords

Wiener index , hyper-Wiener index and Schultz index , circulant network

References

• Bermound, J.C., Comellas, F. and Hsu, D. F. Distributed loop computer networks: survey, J. Parallel Distrib. Comput. 24, 2-10, 1995.
• Boesch, F.T. and Wang, J. Reliable circulant networks with minimum transmission delay, IEEE Transactions on Circuit and Systems 32, 1286-1291, 1985.
• Devillers, J. and Balaban, A.T. (Eds.) Topological indices and related descriptors in QSAR and QSPR (Gordon and Breach, Amsterdam, 1999).
• Diudea, M.V. and Gutman, I. Croat. Chem. Acta 71, 21-51, 1998.
• Klavzar, S. and Gutman, I. A comparison of the Schultz molecular topological index with the Wiener index, J. Chem. Inf. Comut. Sci. 36, 1001-1003, 1996.
• Klein, D.J., Lukovits, I. and Gutman, I. On the definition of the hyper-Wiener index for cycle containing structures, J. Chem. Inf. Comput. Sci. 35, 50-52, 1995.
• Lukovits, I. in: Diudea, M.V. (Ed.) QSAR/QSPR studies by molecular descriptors, Nova, Huntigton, 31-38, 2001.
• Mirzargar, M. and Ashrafi, A.R. Some distance-based topological indices of a non-commuting graph, Hacettepe J. Math. Stat. 41(4), 515-526, 2012.
• Nikolic, S., Trinajstic, N. and Mihalic, Z. The Wiener index: Development and Applications, Croat. Chem. Acta 68, 105-129, 1995.
• Randic, M. Novel molecular description for structure property studies, Chem. Phys. Lett. 211, 478-483, 1993.
• Rouvray, D.H. Should we have designs on topological indices? In Chemical Applications of Topology and Graph Theory; King, B.B. (Ed. 28 Elsevier, Amsterdam, 1984), 159-177.
• Schultz, H.P. Topological organic chemistry 1. Graph theory and topological indices of alkanes, J. Chem. Inf. Comput. Sci. 29, 227-228, 1989.
• Wiener, H. Correlation of heats of isomerization and differences in heats of vaporization of isomers, among the paraffin hydrocarbons, J. Am. Chem. Soc. 69, 17-20, 1947.
• Wong, G.K. and Coppersmith, D.A. A combinatorial problem related to multimodule memory organization, J. Assoc. Comp. Mach. 21, 392-401, 1974.