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Research Articles

M-Polynomials and Topological Indices of Styrene-Butadiene Rubber (SBR)

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Pages 2723-2737 | Received 21 Jul 2020, Accepted 30 Oct 2020, Published online: 09 Dec 2020

References

  • U. Ali, Y. Ahmad, and M. S. Sardar, “On 3-Total Edge Product Cordial Labelling of Tadpole, Book and Flower Graphs,” Open Journal of Mathematical Sciences 4, no. 1 (2020): 48–55.
  • D. Amic, D. Beslo, B. Lucic, S. Nikolic, D. Davidovic-Amicand, and N. Trinajstic, “The Vertex-Connectivity Index Revisited,” Journal of Chemical Information and Computer Science 38, no. 5 (1998): 819–22.
  • Ashaq. Ali, Waqas. Nazeer, Mobeen. Munir, and Shin. Min Kang, “M-Polynomials and Topological Indices of Zigzag and Rhombic Benzenoid Systems,” Open Chemistry 16, no. 1 (2018): 73–8.
  • F. Asif, Z. Zahid, and S. Zafar, “Leap Zagreb and Leap hyper-Zagreb Indices of Jahangir and Jahangir Derived Graphs,” Engineering and Applied Science Letter 3, no. 2 (2020): 1–8.
  • A. T. Balaban, “Highly Discriminating Distance Based Numerical Descripter,” Chemical Physics Letters 89, no. 5 (1982): 399–404.
  • B. Bollobas and P. Erdos, “Graphs of Extremal Weights,” Ars Combinatoria 50 (1998): 225–33.
  • G. Caporossi, I. Gutman, P. Hansen, and L. Pavlovic, “Graphs with Maximum Connectivity Index,” Computational Biology and Chemistry 27, no. 1 (2003): 85–90.
  • K. C. Das and I. Gutman, “Some Properties of the Second Zagreb Index,” MATCH Communications in Mathematical and in Computer Chemistry 52, no. 52 (2004): 103–12.
  • N. De, “On Molecular Topological Properties of TiO2 Nanotubes,” Journal of Nanoscience 2016 (2016): 1–5.
  • E. Deutsch and S. Klavzar “M-Polynomial and Degree-Based Topological Indices, Iran,” Journal of Mathematical Chemistry 6, no. 2 (2015): 93–102.
  • S. Fajtlowicz, “On Conjectures of Graffiti-II,” Proceedings of Congress Numer 60 (1987): 187–97.
  • O. Favaron, M. Maheo, and J. F. Sacle, “Some Eigenvalue Properties in Graphs(Conjectures of graffiti-II),”Discrete Mathematics. 111, no. 1–3 (1993): 197–220. no.
  • B. Furtula, A. Graovac, and D. Vukicevic, “Augmented Zagreb Index,”Journal of Mathematical Chemistry 48, no. 2 (2010): 370–80.
  • W. Gao, Y. Wang, B. Basavanagoud, and M. K. Jamil, “Characteristics Studies of Molecular Structures in Drugs,” Saudi Pharmaceutical Journal: SPJ : The Official Publication of the Saudi Pharmaceutical Society 25, no. 4 (2017): 580–6.
  • C. K. Gupta, V. Lokesha, S. B. Shwetha, and P. S. Ranjini, “On the Symmetric Division Deg Index of Graph,” Southeast Asian Bulletin of Mathematics 40, no. 1 (2016): 59–80.
  • I. Gutman, O.E. Polansky, Mathematical Concepts in Organic Chemistry. Berlin: Springer, 1986.
  • I. Gutman, “Some properties of the Wiener Polynomials,” Graph Theory Notes 125, (1993): 13–18. New York, USA.
  • I. Gutman and K. C. Das, “The First Zagreb Index 30 Years After,” MATCH Communications in Mathematical and in Computer Chemistry 50, no. 50 (2004): 83–92.
  • H. Hosoya, “On Some Cpunting Polynomials in Chemistry,” Discrete Applied Mathematics 19, no. 1–3 (1988): 239–57.
  • Hafiz Muhammad and Afzal. Siddiqui, “Computation of Zagreb Indices and Zagreb Polynomials of Sierpinski Graphs,”Hacettepe Journal of Mathematics and Statistics 49, no. 2 (2020): 754–65.
  • X. Li and I. Gutman, “Mathematical Chemistry Monographs”, Kragujevac, Serbia 1 (2006): VI+330.
  • A. Milicevic, S. Nikolic, and N. Trinajstic, “On Reformulated Zagreb Indices”, Mol. Diversity 8, no. 4 (2004): 393–9.
  • S. Nikolic, G. Kovacevic, A. Milcevic, and N. Trinajstic, ” “The Zagreb Indices 30 Years after,”Croatica Chem. Acta 76, no. 2 (2003): 113–24.
  • P. V. Patil, G. G. Yattinahalli, “Second Zagreb Indices of Transformation Graphs and Total Transformation Graphs,” Open Journal of Discrete Applied Mathematics 3, no. 1 (2020): 1–7.
  • M. Randic, “On Characterization of Molecular Branching,” Journal of the American Chemical Society 97, no. 23 (1975): 6609–15. no.
  • M. Randic, “Quantitative Structure Property Relationship: boiling Points and Planar Benzenoids,” New Journal of Chemistry 20 (1996): 1001–9.
  • Sakander. Hayat, Muhammad. Imran, and Jia-Bao. Liu, “Correlation between the Estrada Index and π-Electron Energies for Benzenoid Hydrocarbons with Applications to Boron Nanotubes,” International Journal of Quantum Chemistry (2019): 1–13.
  • H. F. M. Salih, S. M. Mershkhan, and S. M. Mershkhan, “Generalized the Liouvilles and Mbius Functions of Graph,”Open Journal of Mathematical Sciences 4, no. 1 (2020): 186–94.
  • Sarfraz. Ahmad, Hafiz Muhammad Afzal. Siddiqui, Arfan. Ali, Mohammad R. Farahani, Muhammad. Imran, and Ismail Naci. Cangul, “On Wiener Index and Wiener Polarity Index of Some Polyomino Chains,”Journal of Discrete Mathematical Sciences and Cryptography 22, no. 7 (2019): 1151–64.
  • M. C. Shanmukha, N. S. Basavarajappa, K. N. Anil Kumar, and A. Usha, “ Degree-Based Topological Indices of Dox-Loaded Peg-Pasp Polymer,” Jn˜a¯na¯bha 50, no. 1 (2020): 89–101.
  • M. C. Shanmukha, N. S. Basavarajappa, A. Usha, and K. C. Shilpa, “Novel Neighbourhood Redefined First and Second Zagreb Indices on Carborundum Structures,” Journal of Applied Mathematics and Computing (2020): 1–14.
  • M. C. Shanmukha, N. S. Basavarajappa, K. N. Anilkumar, and K. C. Shilpa, “Generalized Reciprocal Sanskruti Index: Chemical Applicability and Bounds,” Letters in Applied NanoBioScience 9, no. 4 (2020): 1595–601.
  • Shengwei. Deng, Han. Zhuo, Yinbin. Wang, Shuai. Leng, Guilin. Zhuang, Xing. Zhong, Zhongzhe. Wei, Zihao. Yao, and Jian-guo. Wang, “ Multiscale Simulation on Product Distribution from Pyrolysis of Styrene-Butadiene Rubber,” Polymers 11, no. 1967 (2019): 1–14.
  • A. Tabassum, M. A. Umar, M. Perveen, and A. Raheem, “Antimagicness of Subdivided Fans,”Open Journal of Mathematical Sciences 4, no. 1 (2020): 18–22.
  • N. Trinajstic, “Chemical Graph Theory,” Boca Raton, FL: CRC Press 1992.
  • C. Velmurugan and R. Kalaivanan.“Existence of the Golden Ratio in Tanjavur Brihadeeshwarar Temple,”Open Journal of Mathematical Sciences 4, no. 1 (2020): 211–9.
  • D. Vukicevic and A. Graovac, “Valence Connectivity versus Randic, Zagreb and Modified Zagreb Index: A Linear Algorithm to Check Discriminative Properties of Indices in Acyclic Molecular Graphs,” Croatica Chemica Acta 77no. 3 (2004): 501–8. no.
  • D.B. West, “An Introduction to Graph Theory”, Englewood Cliffs, NJ: Prentice-Hall, 1996.
  • Young. Chel Kwun, Mobeen. Munir, Waqas. Nazeer, Shazia. Rafique, and Shin. Min Kang, “M-Polynomials and Topological Indices of V-Phenylenic Nanotubes and Nanotori,” Scientific Reports 7 (2017): 1–9.
  • Young. Chel Kwun, Ashaq. Ali, Waqas. Nazeer, Maqbool Ahmad. Chaudhary, and Shin Min. Kang, “M-Polynomials and Degree-Based Topological Indices of Triangular, Hourglass, and Jagged-Rectangle Benzenoid System,” Journal of Chemistry, Journal of Chemistry 2018 (2018): 1–8.

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