Mathematics Letters

| Peer-Reviewed |

Extremal Chemical Trees of the First Reverse Zagreb Alpha Index

Received: 12 May 2017    Accepted: 28 August 2017    Published: 26 September 2017
Views:       Downloads:

Share This Article

Abstract

Topological indices have important effect to develop chemical sciences by using graph invariants. The Zagreb indices are the most used topological indices in mathematical chemistry literature. Novel forms of Zagreb indices have been extensively defined in recent times. One of the latest version of the Zagreb indices is the reverse Zagreb alpha index. Extremal chemical trees with respect to Zagreb indices have been studied many times in the last two years. In this paper maximum chemical trees were characterized with respect to the first reverse Zagreb alpha index.

DOI 10.11648/j.ml.20170304.12
Published in Mathematics Letters (Volume 3, Issue 4, August 2017)
Page(s) 46-49
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Reverse Zagreb Indices, Zagreb Indices, Topological Index, The First Zagreb Alpha Index, The First Zagreb Beta Index, The Second Reverse Zagreb Index

References
[1] Wiener, H, Structural Determination of Paraffin Boiling Points, J. Am. Chem. Soc., vol. 69, pp. 17-20, 1947.
[2] Gutman. I, Trinajstić, N., Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons, Chem. Phys. Lett., vol. 17, pp. 535-538, 1971.
[3] Gutman, I., Ruščić, B., Trinajstić, N. and Wilcox, C. N., Graph Theory and Molecular Orbitals. XII. Acyclic Polyenes, J. Chem. Phys., vol. 62, pp. 3399-3405, 1975.
[4] Gutman, I., Das, K. C., The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem., vol. 50, pp. 83-92, 2004.
[5] Das, K. C., Gutman, I., Some properties of the second Zagreb index, MATCH Commun. Math. Comput. Chem., vol. 52, pp. 103-112, 2004.
[6] Nikolič, S., Kovačević, G., Miličević, A. and Trinajstić, N., The Zagreb indices 30 years after, Croat. Chem. Acta, vol. 76, pp. 113-124, 2003.
[7] Došlič, T., Furtula, B., Graovac, A., Gutman, I., Moradi, S. and Yarahmadi Z., On Vertex–Degree–Based Molecular Structure Descriptors, MATCH Commun. Math. Comput. Chem., vol. 66, pp. 613-626, 2011.
[8] Vukičevič, Ž. K., Popivoda, G., Chemical Trees with Extreme Values of Zagreb Indices and Coindices, Iranian Journal of Mathematical Chemistry, vol. 5, pp. 19-29, 2014.
[9] Vukičevič, D., Rajtmajer, S. M. and Trinajstić, N.,Trees with maximal second Zagreb index and prescribed number of vertices of the given degree, MATCH Commun. Math. Comput. Chem., vol. 60, pp. 65-70, 2008.
[10] Milavanovic, E. I., Milavanovic, I. Z., Dolicanin, E. C. and Glogic, E., A note on the first reformulated Zagreb index, Appl. Math. and Comp., vol. 273, pp. 16–20, 2016.
[11] Stevanovič, S., On a Relation Between the Zagreb Indices, Croat. Chem. Acta, vol. 84, pp. 17-19, 2011.
[12] Ediz, S., Maximum chemical trees of the second reverse Zagreb index, Pacific Journal of Applied Mathematics, vol. 7,pp. 291-295, 2015.
[13] Farahani, Mohammad Reza, R. Pradeep Kumar, and MR Rajesh Kanna. "First and second Zagreb indices and polynomials of v-phenylenic nanotubes and nanotori." International Journal of Pharmaceutical Sciences and Research 8.1 (2017): 330.
[14] Ghobadi, S., and M. Ghorbaninejad. "First Zagreb Index, F-index and F-coindex of the Line Subdivision Graphs." Turkish Journal of Analysis and Number Theory 5.1 (2017): 23-26.
[15] Basavanagoud, B., and Sujata Timmanaikar. "Computing First Zagreb and Forgotten Indices of Certain Dominating Transformation Graphs of Kragujevac Trees." Journal of Computer and Mathematical Sciences 8.3 (2017): 50-61.
[16] Gao, W., Jamil, M. K., Javed, A., Farahani, M. R., Wang, S., & Liu, J. B. (2017). Sharp Bounds of the Hyper-Zagreb Index on Acyclic, Unicylic, and Bicyclic Graphs. Discrete Dynamics in Nature and Society, 2017.
[17] Shafique, S., & Ali, A. (2017). On the reduced second Zagreb index of trees. Asian-European Journal of Mathematics, 1750084.
[18] Li, Y., Yan, L., Jamil, M. K., Farahani, M. R., Gao, W., & Liu, J. B. (2017). Four New/Old Vertex-Degree-Based Topological Indices of HAC5C7 [p, q] and HAC 5 C 6 C 7 [p, q] Nanotubes. Journal of Computational and Theoretical Nanoscience, 14(1), 796-799.
[19] Ajmal, M., Nazeer, W., Khalid, W., & Kang, S. M. (2017). Zagreb Polynomials and Multiple Zagreb Indices for the Line Graphs of Banana Tree Graph, Firecracker Graph and Subdivision Graphs. Global Journal of Pure and Applied Mathematics, 13(6), 2659-2672.
[20] Aslam, A., Bashir, Y., Rafiq, M., Haider, F., Muhammad, N., & Bibi, N. (2017). Three New/Old Vertex-Degree-Based Topological Indices of Some Dendrimers Structure. Electronic Journal of Biology.
[21] Ajmal, M., Nazeer, W., Munir, M., Kang, S. M., & Jung, C. Y. (2017). The M-Polynomials and Topological Indices of Toroidal Polyhex Network. International Journal of Mathematical Analysis, 11(7), 305-315.
[22] Sarala, D., Deng, H., Ayyaswamy, S. K., & Balachandran, S. (2017). The Zagreb indices of graphs based on four new operations related to the lexicographic product. Applied Mathematics and Computation, 309, 156-169.
[23] Gorji, A. E., Gorji, Z. E., & Riahi, S. (2017). Quantitative structure-property relationship (QSPR) for prediction of CO2 Henry’s law constant in some physical solvents with consideration of temperature effects. Korean Journal of Chemical Engineering, 1-11.
[24] Doslic, T., Sedghi, S., & Shobe, N. (2017). Stirling Numbers and Generalized Zagreb Indices. Iranian Journal of Mathematical Chemistry, 8(1), 1-5.
[25] Ali, A., & Trinajstić, N. (2017). A Novel/Old Modification of the First Zagreb Index. arXiv preprint arXiv:1705.10430.
[26] Gutman, I., Kulli, V. R., Chaluvaraju, B., & Boregowda, H. S. (2017). On Banhatti and Zagreb indices. Journal of International Mathematical Virtual Institute, 7(1), 53-67.
Author Information
  • Department of Mathematics, Faculty of Education, Van Yüzüncü Y?l University, Van, Turkey

Cite This Article
  • APA Style

    Süleyman Ediz. (2017). Extremal Chemical Trees of the First Reverse Zagreb Alpha Index. Mathematics Letters, 3(4), 46-49. https://doi.org/10.11648/j.ml.20170304.12

    Copy | Download

    ACS Style

    Süleyman Ediz. Extremal Chemical Trees of the First Reverse Zagreb Alpha Index. Math. Lett. 2017, 3(4), 46-49. doi: 10.11648/j.ml.20170304.12

    Copy | Download

    AMA Style

    Süleyman Ediz. Extremal Chemical Trees of the First Reverse Zagreb Alpha Index. Math Lett. 2017;3(4):46-49. doi: 10.11648/j.ml.20170304.12

    Copy | Download

  • @article{10.11648/j.ml.20170304.12,
      author = {Süleyman Ediz},
      title = {Extremal Chemical Trees of the First Reverse Zagreb Alpha Index},
      journal = {Mathematics Letters},
      volume = {3},
      number = {4},
      pages = {46-49},
      doi = {10.11648/j.ml.20170304.12},
      url = {https://doi.org/10.11648/j.ml.20170304.12},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ml.20170304.12},
      abstract = {Topological indices have important effect to develop chemical sciences by using graph invariants. The Zagreb indices are the most used topological indices in mathematical chemistry literature. Novel forms of Zagreb indices have been extensively defined in recent times. One of the latest version of the Zagreb indices is the reverse Zagreb alpha index. Extremal chemical trees with respect to Zagreb indices have been studied many times in the last two years. In this paper maximum chemical trees were characterized with respect to the first reverse Zagreb alpha index.},
     year = {2017}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Extremal Chemical Trees of the First Reverse Zagreb Alpha Index
    AU  - Süleyman Ediz
    Y1  - 2017/09/26
    PY  - 2017
    N1  - https://doi.org/10.11648/j.ml.20170304.12
    DO  - 10.11648/j.ml.20170304.12
    T2  - Mathematics Letters
    JF  - Mathematics Letters
    JO  - Mathematics Letters
    SP  - 46
    EP  - 49
    PB  - Science Publishing Group
    SN  - 2575-5056
    UR  - https://doi.org/10.11648/j.ml.20170304.12
    AB  - Topological indices have important effect to develop chemical sciences by using graph invariants. The Zagreb indices are the most used topological indices in mathematical chemistry literature. Novel forms of Zagreb indices have been extensively defined in recent times. One of the latest version of the Zagreb indices is the reverse Zagreb alpha index. Extremal chemical trees with respect to Zagreb indices have been studied many times in the last two years. In this paper maximum chemical trees were characterized with respect to the first reverse Zagreb alpha index.
    VL  - 3
    IS  - 4
    ER  - 

    Copy | Download

  • Sections