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

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

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.

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

Abstract

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.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Faisal Ali

Abdul Hafeez This is me

Muhammad Salman This is me

Shuliang Huang

Publication Date December 12, 2018
Published in Issue Year 2018 Volume: 47 Issue: 6

Cite

APA Ali, F., Hafeez, A., Salman, M., Huang, S. (2018). On computation of some distance-based topological indices of circulant networks. Hacettepe Journal of Mathematics and Statistics, 47(6), 1427-1437.
AMA Ali F, Hafeez A, Salman M, Huang S. On computation of some distance-based topological indices of circulant networks. Hacettepe Journal of Mathematics and Statistics. December 2018;47(6):1427-1437.
Chicago Ali, Faisal, Abdul Hafeez, Muhammad Salman, and Shuliang Huang. “On Computation of Some Distance-Based Topological Indices of Circulant Networks”. Hacettepe Journal of Mathematics and Statistics 47, no. 6 (December 2018): 1427-37.
EndNote Ali F, Hafeez A, Salman M, Huang S (December 1, 2018) On computation of some distance-based topological indices of circulant networks. Hacettepe Journal of Mathematics and Statistics 47 6 1427–1437.
IEEE F. Ali, A. Hafeez, M. Salman, and S. Huang, “On computation of some distance-based topological indices of circulant networks”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 6, pp. 1427–1437, 2018.
ISNAD Ali, Faisal et al. “On Computation of Some Distance-Based Topological Indices of Circulant Networks”. Hacettepe Journal of Mathematics and Statistics 47/6 (December 2018), 1427-1437.
JAMA Ali F, Hafeez A, Salman M, Huang S. On computation of some distance-based topological indices of circulant networks. Hacettepe Journal of Mathematics and Statistics. 2018;47:1427–1437.
MLA Ali, Faisal et al. “On Computation of Some Distance-Based Topological Indices of Circulant Networks”. Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 6, 2018, pp. 1427-3.
Vancouver Ali F, Hafeez A, Salman M, Huang S. On computation of some distance-based topological indices of circulant networks. Hacettepe Journal of Mathematics and Statistics. 2018;47(6):1427-3.