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