SavedAdd your journal

Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2019 / Volume: 68 Issue: 2

The M-polynomial of line graph of subdivision graphs

Sourav Mondal0000-0003-1928-7075
Nilanjan De0000-0003-1928-7075
Anita Pal0000-0002-2514-5463
Pages
—
Publication Date
2019-08-01
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In this report, we first determine M-polynomial of the Line graph of those three graphs using subdivision idea and then compute some degree based indices of the same.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Three composite graphs Ladder graph (L_{n}), Tadpole graph (T_{n,k}) and Wheel graph (W_{n}) are graceful graphs, which have different applications in electrical, electronics, wireless communication etc.
📊
Key Findings & Data:Three composite graphs Ladder graph (L_{n}), Tadpole graph (T_{n,k}) and Wheel graph (W_{n}) are graceful graphs, which have different applications in electrical, electronics, wireless communication etc.
💡
Conclusion & Impact:In this report, we first determine M-polynomial of the Line graph of those three graphs using subdivision idea and then compute some degree based indices of the same.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:M-polynomial · degree based topological index · line graph

Abstract

Three composite graphs Ladder graph (L_{n}), Tadpole graph (T_{n,k}) and Wheel graph (W_{n}) are graceful graphs, which have different applications in electrical, electronics, wireless communication etc. In this report, we first determine M-polynomial of the Line graph of those three graphs using subdivision idea and then compute some degree based indices of the same.

🔖

Cite This Article

Mondal, S., De, N., Pal, A. (2019). The M-polynomial of line graph of subdivision graphs. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 68 Issue: 2. https://doi.org/10.31801/cfsuasmas.587655

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (24)

  1. Deutsch, E. and Klavzar, S., M-Polynomial, and degree-based topological indices, Iran. J. Math. Chem., 6,(2015), 93-102.
  2. Gutman, I., Some properties of the Wiener polynomials, Graph Theory Notes N.Y., 125, (1993), 13-18.
  3. Alamian, V., Bahrami, A. and Edalatzadeh, B., PI Polynomial of V-Phenylenic nanotubes and nanotori, Int. J. Mole. Sci. 9(3), (2008), 229-234. doi: 10.3390/ijms9030229.
  4. Farahani, MR., Computing theta polynomial, and theta index of V-phenylenic planar, nanotubes and nanotoris, Int. J. Theoretical Chem., 1(1), (2013), 01-09.
  5. Munir, M., Nazeer, W., Shahzadi, S. and Kang, SM., Some invariants of circulant graphs, Symmetry, 8(11), (2016), 134. doi: 10.3390/sym8110134.
  6. Rajan, M.A., Lokesha, V. and Ranjini, P.S., A Study on Series Edge Graph Transformation, Proc. 23rd Joint Congress Iran-South Korea Jangjeon Math. Soc.,Iran, (2010).
  7. Ranjini, P.S., Lokesha, V. and Rajan, M.A., On Zagreb indices of the subdivision graphs, Int. J. Math. Sci. Eng. Appl., (2010), 4, 221-228.
  8. Ranjini, P.S., Lokesha, V. and Rajan, M.A., On Zagreb indices of the p-subdivision graphs, J. Oriss. Math. Soc., (2010), appear.
  9. Gutman, I., Lee, Y-N., Yeh Y.N. and Lau, Y.L., Some recent results in the theory of Wiener number, Ind. J. Chem., 32,(1993), 551-661.
  10. Douglas, B.W., Introduction to Graph Theory, second ed., Prentice Hall, 2001.
  11. Weisstein, E.W., Tadpole Graph, Mathworld-A Wolfram Web Resource.
  12. Ranjini, P.S., Lokesha, V. and Cangıl, I.N., On the Zagreb indices of the line graphs of the subdivision graphs, Applied Mathematics and Computation, (2011), 218, 699-702.
  13. Su, Guifu, Xu, Lan, Topological indices of the line graph of subdivision graphs and their Schur-bounds, Applied Mathematics and Computation, (2015), 395-401.
  14. Gutman, I., Degree-based topological indices, Croat. Chem. Acta, 86, (2013), 351-361.
  15. Gutman, I. and Trinajstic, N., Graph theory and molecular orbitals total φ-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17,(1972), pp. 535-538.
  16. Bollobas, B. and Erdös, P., Graphs of extremal weights, Ars Combin., 50,(1998), pp.225-233.
  17. Amic, D., Beslo, D., Lucic, B., Nikolic, S. and Trinajstiác, N., The vertex-connectivity index revisited, J. Chem. Inf. Comput. Sci., 38,(1998), pp. 819-822.
  18. Hu, Y., Li, X., Shi, Y., Xu, T. and Gutman, I., On molecular graphs with smallest and greatest zeroth-Corder general Randiác index, MATCH Commun. Math. Comput.Chem., 54,(2005), pp. 425-434.
  19. Caporossi, G., Gutman, I., Hansen, P. and Pavlovic, L., Graphs with maximum connectivity index, Comput. Biol. Chem., 27,(2003), pp. 85-90.
  20. Li, X. and Gutman, I., Mathematical aspects of Randiac-type molecular structure descriptors, Mathematical Chemistry Monographs, No. 1, Publisher Univ. Kragujevac, Kragujevac, 2006.
  21. Fajtlowicz, S., On conjectures of Graffiti II, Congr. Numer., 60,(1987), pp. 189-197.
  22. Balaban, A. T., Highly discriminating distance based numerical descriptor, Chem.Phys. Lett., 89,(1982), pp. 399-404.
  23. Furtula, B., Graovac, A. and Vukićević, D., Augmented Zagreb index, J. Math. Chem., 48 (2010), pp. 370-380.
  24. Munir, M., Nazeer, W., Shahzadi, S. and Kang, SM., Some invariants of circulant graphs, Symmetry, 8(11), (2016), 134. doi: 10.3390/sym8110134.