Year 2020,
Volume: 8 Issue: 1, 97 - 105, 15.04.2020
Sourav Mondal
Nilanjan De
,
Anita Pal
References
- [1] E. Deutsch and S. Klavzar, M-Polynomial, and degree-based topological indices, Iran. J. Math. Chem., Vol:6,(2015), 93-102.
- [2] I. Gutman, Some properties of the Wiener polynomials, Graph Theory Notes N.Y., Vol:125, (1993), 13-18.
- [3] V. Alamian ,A. Bahrami and B. Edalatzadeh, PI Polynomial of V-Phenylenic nanotubes and nanotori, Int. J. Mole. Sci., Vol:9, (2008), 229-234. doi:
10.3390/ijms9030229.
- [4] M. R. Farahani, Computing theta polynomial, and theta index of V-phenylenic planar, nanotubes and nanotoris, Int. J. Theoretical Chem., Vol:1, No.1,
(2013), 01-09.
- [5] M. Munir,W. Nazeer, S. Shahzadi and S. M. Kang , Some invariants of circulant graphs, Symmetry, Vol:8, No.11, (2016), 134. doi: 10.3390/sym8110134.
- [6] I. Gutman, Degree-based topological indices, Croat. Chem. Acta, Vol:86, (2013), 351-361.
- [7] I. Gutman and N. Trinajstic, Graph theory and molecular orbitals total p-electron energy of alternant hydrocarbons, Chem. Phys. Lett., Vol:17,(1972),
535-538.
- [8] B. Bollobas and P. Erd¨os, Graphs of extremal weights, Ars Combin., Vol:50,(1998), 225-233.
- [9] D. Amic, D. Beslo, B. Lucic, S. Nikolic and N. Trinajsti´c, The vertex-connectivity index revisited, J. Chem. Inf. Comput. Sci., Vol:38,(1998), 819-822.
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Comput.Chem., Vol:54,(2005), pp. 425-434.
- [11] X. Li and I. Gutman, Mathematical aspects of Randic-type molecular structure descriptors, Mathematical Chemistry Monographs, No. 1, Publisher Univ.
Kragujevac, Kragujevac, (2006).
- [12] G. Caporossi, I. Gutman, P. Hansen and L. Pavlovic, Graphs with maximum connectivity index, Comput. Biol. Chem., Vol:27,(2003), 85-90.
- [13] S. Fajtlowicz, On conjectures of Graffiti II, Congr. Numer., Vol:60,(1987), 189-197.
- [14] A. T. Balaban, Highly discriminating distance based numerical descriptor, Chem.Phys. Lett., Vol:89,(1982), 399-404.
- [15] B. Furtula, A. Graovac and D.Vuki´cevi´c, Augmented Zagreb index, J. Math. Chem., Vol:48, (2010), 370-380.
- [16] M.O Keeffe, G. B. Adams, and O. F. Sankey, Predicted new low energy forms of carbon, Phys. Rev. Lett., Vol:68, (1992), 2325-2328.
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- [18] M. V. Diudea, Cs. L. Nagy, Periodic Nanostructures, Springer, Dordrecht, (2007).
- [19] I. Stojmenovic, Honeycomb Networks: Topological Properties and Communication Algorithms, IEEE Trans. Parallel Distrib. Syst., Vol:8, (1997),
1036-1042.
- [20] A. Ahmad, On the degree based topological indices of benzene ring embedded in P-type-surface in 2D network, Hacettepe Journal of Mathematics and
Statistics, Vol:47,(2018), 9-18.
- [21] M. Imran, M. K. Siddiqui, A. Ahmad, U. Ali, and N. Hanif, On the Degree-Based Topological Indices of the Tickysim SpiNNaker Model, Axioms,
Vol:7,(2018), 73-85.
- [22] Y. C. Kwun, M. Munir, W. Nazeer, S. Rafque and S. M. Kang, M-Polynomials and topological indices of V-Phenylenic Nanotubes and Nanotori,
Scientific Reports, Vol:7, (2017), doi:10.1038/s41598-017-08309-y.
- [23] S. Mondal, N. De, and A. Pal, The M-Polynomial of Line graph of Subdivision graphs, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., Vol:68,
No.2, (2019), 2104-2116.
- [24] M. S. Ahmad, W. Nazeer, S. M. Kang, and C. Y. Jung, M-polynomials and Degree based Topological Indices for the Line Graph of Firecracker Graph,
Global Journal of Pure and Applied Mathematics, Vol:13, (2017), 2749-2776.
- [25] M. Munir, W. Nazeer, S. Rafique, and S. M. Kang, M-Polynomial and Degree-Based Topological Indices of Polyhex Nanotubes, Symmetry, Vol:8,
(2016), doi:10.3390/sym8120149.
- [26] M. Munir, W. Nazeer, S. M. Kang, M. I. Qureshi , A. R. Nizami, and Y. C. Kwun, Some Invariants of Jahangir Graphs, Symmetry, Vol:9, (2017),
doi:10.3390/sym9010017.
- [27] A. Verma, S. Mondal, N. De, and A. Pal, Topological Properties of Bismuth tri-iodide Using Neighborhood M-Polynomial , International Journal of
Mathematics Trends and Technology, Vol:65, (2019), 83-90.
Topological Properties of Networks Using M-Polynomial Approach
Year 2020,
Volume: 8 Issue: 1, 97 - 105, 15.04.2020
Sourav Mondal
Nilanjan De
,
Anita Pal
Abstract
The M-polynomial is one of the algebraic polynomials, that is useful in theoretical chemistry. It plays significant role in computing the exact expressions of many degree based topological indices. In this report, the M-polynomial of the benzene ring embedded in P-type-surface in 2D network and the Tickysim SpiNNaker Model (TSM) sheet are derived. Using those M-polynomials, some degree based topological indices are derived. In addition, the results are interpreted graphically.
Supporting Institution
NIT Durgapur, India.
Thanks
The first author is very obliged to the Department of Science and Technology (DST), Government of India for the Inspire Fellowship [IF170148]
References
- [1] E. Deutsch and S. Klavzar, M-Polynomial, and degree-based topological indices, Iran. J. Math. Chem., Vol:6,(2015), 93-102.
- [2] I. Gutman, Some properties of the Wiener polynomials, Graph Theory Notes N.Y., Vol:125, (1993), 13-18.
- [3] V. Alamian ,A. Bahrami and B. Edalatzadeh, PI Polynomial of V-Phenylenic nanotubes and nanotori, Int. J. Mole. Sci., Vol:9, (2008), 229-234. doi:
10.3390/ijms9030229.
- [4] M. R. Farahani, Computing theta polynomial, and theta index of V-phenylenic planar, nanotubes and nanotoris, Int. J. Theoretical Chem., Vol:1, No.1,
(2013), 01-09.
- [5] M. Munir,W. Nazeer, S. Shahzadi and S. M. Kang , Some invariants of circulant graphs, Symmetry, Vol:8, No.11, (2016), 134. doi: 10.3390/sym8110134.
- [6] I. Gutman, Degree-based topological indices, Croat. Chem. Acta, Vol:86, (2013), 351-361.
- [7] I. Gutman and N. Trinajstic, Graph theory and molecular orbitals total p-electron energy of alternant hydrocarbons, Chem. Phys. Lett., Vol:17,(1972),
535-538.
- [8] B. Bollobas and P. Erd¨os, Graphs of extremal weights, Ars Combin., Vol:50,(1998), 225-233.
- [9] D. Amic, D. Beslo, B. Lucic, S. Nikolic and N. Trinajsti´c, The vertex-connectivity index revisited, J. Chem. Inf. Comput. Sci., Vol:38,(1998), 819-822.
- [10] Y. Hu, X. Li,Y. Shi, T. Xu and I. Gutman, On molecular graphs with smallest and greatest zeroth-Corder general Randi´c index, MATCH Commun. Math.
Comput.Chem., Vol:54,(2005), pp. 425-434.
- [11] X. Li and I. Gutman, Mathematical aspects of Randic-type molecular structure descriptors, Mathematical Chemistry Monographs, No. 1, Publisher Univ.
Kragujevac, Kragujevac, (2006).
- [12] G. Caporossi, I. Gutman, P. Hansen and L. Pavlovic, Graphs with maximum connectivity index, Comput. Biol. Chem., Vol:27,(2003), 85-90.
- [13] S. Fajtlowicz, On conjectures of Graffiti II, Congr. Numer., Vol:60,(1987), 189-197.
- [14] A. T. Balaban, Highly discriminating distance based numerical descriptor, Chem.Phys. Lett., Vol:89,(1982), 399-404.
- [15] B. Furtula, A. Graovac and D.Vuki´cevi´c, Augmented Zagreb index, J. Math. Chem., Vol:48, (2010), 370-380.
- [16] M.O Keeffe, G. B. Adams, and O. F. Sankey, Predicted new low energy forms of carbon, Phys. Rev. Lett., Vol:68, (1992), 2325-2328.
- [17] M. V. Diudea (Ed.), Nanostructures, Novel Architecture, NOVA, New York, (2005).
- [18] M. V. Diudea, Cs. L. Nagy, Periodic Nanostructures, Springer, Dordrecht, (2007).
- [19] I. Stojmenovic, Honeycomb Networks: Topological Properties and Communication Algorithms, IEEE Trans. Parallel Distrib. Syst., Vol:8, (1997),
1036-1042.
- [20] A. Ahmad, On the degree based topological indices of benzene ring embedded in P-type-surface in 2D network, Hacettepe Journal of Mathematics and
Statistics, Vol:47,(2018), 9-18.
- [21] M. Imran, M. K. Siddiqui, A. Ahmad, U. Ali, and N. Hanif, On the Degree-Based Topological Indices of the Tickysim SpiNNaker Model, Axioms,
Vol:7,(2018), 73-85.
- [22] Y. C. Kwun, M. Munir, W. Nazeer, S. Rafque and S. M. Kang, M-Polynomials and topological indices of V-Phenylenic Nanotubes and Nanotori,
Scientific Reports, Vol:7, (2017), doi:10.1038/s41598-017-08309-y.
- [23] S. Mondal, N. De, and A. Pal, The M-Polynomial of Line graph of Subdivision graphs, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., Vol:68,
No.2, (2019), 2104-2116.
- [24] M. S. Ahmad, W. Nazeer, S. M. Kang, and C. Y. Jung, M-polynomials and Degree based Topological Indices for the Line Graph of Firecracker Graph,
Global Journal of Pure and Applied Mathematics, Vol:13, (2017), 2749-2776.
- [25] M. Munir, W. Nazeer, S. Rafique, and S. M. Kang, M-Polynomial and Degree-Based Topological Indices of Polyhex Nanotubes, Symmetry, Vol:8,
(2016), doi:10.3390/sym8120149.
- [26] M. Munir, W. Nazeer, S. M. Kang, M. I. Qureshi , A. R. Nizami, and Y. C. Kwun, Some Invariants of Jahangir Graphs, Symmetry, Vol:9, (2017),
doi:10.3390/sym9010017.
- [27] A. Verma, S. Mondal, N. De, and A. Pal, Topological Properties of Bismuth tri-iodide Using Neighborhood M-Polynomial , International Journal of
Mathematics Trends and Technology, Vol:65, (2019), 83-90.