DOI QR코드

DOI QR Code

COMPUTATION OF SOMBOR INDICES OF OTIS(BISWAPPED) NETWORKS

  • Basavanagoud, B. (Department of Mathematics Karnatak University) ;
  • Veerapur, Goutam (Department of Mathematics Karnatak University)
  • 투고 : 2022.01.31
  • 심사 : 2022.06.29
  • 발행 : 2022.08.15

초록

In this paper, we derive analytical closed results for the first (a, b)-KA index, the Sombor index, the modified Sombor index, the first reduced (a, b)-KA index, the reduced Sombor index, the reduced modified Sombor index, the second reduced (a, b)-KA index and the mean Sombor index mSOα for the OTIS biswapped networks by considering basis graphs as path, wheel graph, complete bipartite graph and r-regular graphs. Network theory plays a significant role in electronic and electrical engineering, such as signal processing, networking, communication theory, and so on. A topological index (TI) is a real number associated with graph networks that correlates chemical networks with a variety of physical and chemical properties as well as chemical reactivity. The Optical Transpose Interconnection System (OTIS) network has recently received increased interest due to its potential uses in parallel and distributed systems.

키워드

과제정보

This work was supported by Karnatak University, Dharwad, Karnataka India, through University Research Studentship (URS), No.KU.40(SC/ST)sch/URS/2020-21/44/533, dated 12.12.2020.

참고문헌

  1. A. Aslam, S. Ahmad, M. A. Binyamin and W. Gao, Calculating topological indices of certain OTIS interconnection networks, Open Chem. 17 (2019), 220-228. https://doi.org/10.1515/chem-2019-0029
  2. A. Al-Ayyoub, A. Awwad, K. Day and M. Ould-Khaoua, Generalized methods for algorithm development on optical systems, J. Supercomputing, 38 (2006), 111-125. https://doi.org/10.1007/s11227-006-7447-6
  3. B. Basavanagoud and G. Veerapur, On second order graph indices of certain OTIS networks, Des. Eng. 8 (2021), 13814-13832.
  4. G. Chartrand and L. Lesniak, Graphs and Digraphs, CHAPMAN & HALL/CRC, 1996.
  5. J. Chen, J. Liu and X. Guo, Some upper bounds for the atombond connectivity index of graphs, Appl. Math. Lett. 25 (2012), no. 7, 1077-1081. https://doi.org/10.1016/j.aml.2012.03.021
  6. K. Day and A. Al-Ayyoub, Topological properties of OTIS-networks, IEEE T. Parall. Distr. Syst. 14 (2002), 359-366.
  7. T. Deepika and V. Lokesha, Computing Discrete Adriatic indices of Probabilistic Neural Networks, Eur. J. Pure Appl. Math. 13 (2020), no. 5, 1149-1161. https://doi.org/10.29020/nybg.ejpam.v13i5.3712
  8. I. Gutman, Geometric approach to degree-based topological indices:Sombor indices, MATCH Common, Math. Comput. Chem. 86 (2021), 11-16.
  9. F. Harary, Graph Theory, Addison-Wesley, Reading, 1969.
  10. P. K. Jana and B. P. Sinha, An improved parallel prefix algorithm on OTIS-mesh, Parall. Proc. Leters. 16 (2006), 429-440.
  11. P. K. Jana, Polynomial interpolation and polynomial root finding on OTIS-mesh, Parall. Comput. 32 (2006), 301-312. https://doi.org/10.1016/j.parco.2006.01.001
  12. S. Rajasekaran and S. Sahni, Randomized routing, selection and sorting on the OTIS-mesh, IEEE T. Parall. Distr. Syst. 9 (1998), 833-840. https://doi.org/10.1109/71.722217
  13. V. R. Kull and I. Gutman, Computation of Sombor Indices of Certain Networks, Int. J. Appl. Chem. 8 (2021), no. 1, 1-5.
  14. G. Marsden, P. Marchand, P. Harvey, and S. Esener, Optical transpose interconnection system architecture, Opt. Lett. 18 (1993), 1083-1085. https://doi.org/10.1364/OL.18.001083
  15. J. A. Mendez-Bermudez, R. Arguialr-Sanchez, E. D. Molina and J. M. Rodriguez, Mean Sombor index, Discrete Math. Lett. 9 (2022), 18-25.
  16. P. G. Sheeja, P. S. Ranjini, V. Lokesha and A. Sinan Cevik, M Polynomials and topological indices of Benzene ring embedded in p-type surface in networks, Chin. J. Math. Sci. 1 (2021), no. 1, 39-47.
  17. H. Wiener, Structural determination of paraffin boiling points, J. Amer. Chem. Soc. 69 (1947), no. 1, 17-20. https://doi.org/10.1021/ja01193a005
  18. C. F. Wang and S. Sahni, Basic operations on the OTIS-Mesh optoelectronic computer, IEEE T. Parall. Distr. Syst. 9 (1998), 1226-1236. https://doi.org/10.1109/71.737698
  19. C. F. Wang and S. Sahni, OTIS optoelectronic computers, Chapter 5 in Parallel Computation Using Optical Interconnection, K. Li, Y. Pan and S.Q. Zhang, eds., Kluwer Academic Publishers, (1998), 99-116.
  20. C. F. Wang and S. Sahni, Matrix multiplication on the OTISMesh optoelectronic computer, IEEE T. Comput. 50 (2001), 635-646. https://doi.org/10.1109/12.936231
  21. C. F. Wang and S. Sahni, Image processing on the OTIS-Mesh optoelectronic computer, IEEE T. Parall. Distr. Syst. 11 (2000), 97-109. https://doi.org/10.1109/71.841747
  22. B. Zhou and N. Trinajstic, On general sum-connectivity index, J. Math. Chem. 47 (2010), no. 1, 210-218. https://doi.org/10.1007/s10910-009-9542-4