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Some Degree-Based Topological Indices of Base-3 Sierpiński Graphs

Received: 3 June 2017     Accepted: 4 July 2017     Published: 31 July 2017
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Abstract

In this paper, a recursive relation between base-3 Sierpiński graphs rank n and n-1 of some topostructural indices is studied. Based on this relation, The formulae of the First Zagreb index, Second Zagreb index, Randić connectivity index, sum-connectivity index, Geometric-Arithmetic index and Atom-Bond Connectivity index of base-3 Sierpiński graphs are derived.

Published in Science Journal of Chemistry (Volume 5, Issue 3)
DOI 10.11648/j.sjc.20170503.12
Page(s) 36-41
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), 2017. Published by Science Publishing Group

Keywords

Topological Index, Base-3 Sierpiński Graphs, Zagreb Index, Sum-Connectivity Index, Geometric-Arithmetic Index, Atom-Bond Connectivity Index, Sankruti Index

References
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[2] Darafsheh, M. R. Computation of Topological Indices of Some Graphs. Acta Appl. Math. 2010; 110; 1225–1235.
[3] Vukicevic, D., Furtula, B. Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges, J. Math. Chem. 2009; 46; 1369–1376.
[4] Estrada, E., Torres, L., Rodriguez, L., Gutman, I. An atom–bond connectivity index: modelling the enthalpy 128of formation of alkanes. Indian J. Chem. Sect. 1998; 37; 849–855.
[5] Hinz, A. M., Klavzar, S., Zemljic, S. S. A survey and classification of Sierpinski-type graphs. Discrete Appl. 2017; 217; 565-600.
[6] Gutman, I., Das, K. C. The first Zagreb indices 30 years after, MATCH Commun. Math. Comput. Chem. 2004; 50; 83–92.
[7] Gutman, I., Trinajstic, N. Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 1972; 17; 535–538.
[8] Rodriguez, J. M., Sigarreta, J. M. On the Geometric-Arithmetic Index. MATCH Commun. Math. Comput. Chem. 2015; 74; 103–120.
[9] Klavzar, Sandi, Milutinovic, U. Graphs S (n, k), and a Variant of the Tower of Hanoi Problem. Czech. Math. J. 1997; 47; 95–104.
[10] Randic, M. The connectivity index 25 years later. J. Mol. Graph. Model. 2001; 20; 19–35.
[11] Tomasz, P., Leszczynski, J., Mark, T. C. Molecular Descriptors, In Recent advances in QSAR studies: methods and applications; Jerzy L. Eds.; Springer Science & Business Media: Heidelberg, Germany, 2010; pp. 39.
[12] Randic, Milan. Characterization of molecular branching. J. Am. Chem. Soc. 1975; 97; 6609-6615.
[13] Nikolc, S., Kovacevic, G., Milicevic, A., Trinajstic, N. The Zagreb indices 30 years after, Croat. Chem. Acta. 2003; 76; 113–124.
[14] Wiener, H. Correlation of Heats of Isomerization, and Differences in Heats of Vaporization of Isomers, Among the Paraffin Hydrocarbons. J. Am. Chem. Soc. 1947; 84; 2636–2638.
[15] Zhou, B., Trinajstic, N. On a novel connectivity index. J. Math. Chem. 2009, 46, 1252–1270.
[16] Lucic, B., Trinajstic, N., Zhou, B. Comparison between the sum-connectivity index and product-connectivity index for benzenoid hydrocarbons. Chem. Phy. Let. 2009; 475; 146–148.
[17] Fath-Tabar, G., Furtula, B., Gutman, I. A new geometric–arithmetic index. J. Math. Chem. 2010; 47; 477–486.
[18] Estradamoreno, A., Rodríguezbazan, E. D., Rodríguezvelazquez, J. A. (2015). On the general randic index of polymeric networks modelled by generalized sierpiński graphs. MATCH Commun. Math. Comput. Chem. 2015; 74; 145–160.
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  • APA Style

    Xiujun Zhang, Hong Yang, Yingying Gao, Mohammad Reza Farahani. (2017). Some Degree-Based Topological Indices of Base-3 Sierpiński Graphs. Science Journal of Chemistry, 5(3), 36-41. https://doi.org/10.11648/j.sjc.20170503.12

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    ACS Style

    Xiujun Zhang; Hong Yang; Yingying Gao; Mohammad Reza Farahani. Some Degree-Based Topological Indices of Base-3 Sierpiński Graphs. Sci. J. Chem. 2017, 5(3), 36-41. doi: 10.11648/j.sjc.20170503.12

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    AMA Style

    Xiujun Zhang, Hong Yang, Yingying Gao, Mohammad Reza Farahani. Some Degree-Based Topological Indices of Base-3 Sierpiński Graphs. Sci J Chem. 2017;5(3):36-41. doi: 10.11648/j.sjc.20170503.12

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  • @article{10.11648/j.sjc.20170503.12,
      author = {Xiujun Zhang and Hong Yang and Yingying Gao and Mohammad Reza Farahani},
      title = {Some Degree-Based Topological Indices of Base-3 Sierpiński Graphs},
      journal = {Science Journal of Chemistry},
      volume = {5},
      number = {3},
      pages = {36-41},
      doi = {10.11648/j.sjc.20170503.12},
      url = {https://doi.org/10.11648/j.sjc.20170503.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjc.20170503.12},
      abstract = {In this paper, a recursive relation between base-3 Sierpiński graphs rank n and n-1 of some topostructural indices is studied. Based on this relation, The formulae of the First Zagreb index, Second Zagreb index, Randić connectivity index, sum-connectivity index, Geometric-Arithmetic index and Atom-Bond Connectivity index of base-3 Sierpiński graphs are derived.},
     year = {2017}
    }
    

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  • TY  - JOUR
    T1  - Some Degree-Based Topological Indices of Base-3 Sierpiński Graphs
    AU  - Xiujun Zhang
    AU  - Hong Yang
    AU  - Yingying Gao
    AU  - Mohammad Reza Farahani
    Y1  - 2017/07/31
    PY  - 2017
    N1  - https://doi.org/10.11648/j.sjc.20170503.12
    DO  - 10.11648/j.sjc.20170503.12
    T2  - Science Journal of Chemistry
    JF  - Science Journal of Chemistry
    JO  - Science Journal of Chemistry
    SP  - 36
    EP  - 41
    PB  - Science Publishing Group
    SN  - 2330-099X
    UR  - https://doi.org/10.11648/j.sjc.20170503.12
    AB  - In this paper, a recursive relation between base-3 Sierpiński graphs rank n and n-1 of some topostructural indices is studied. Based on this relation, The formulae of the First Zagreb index, Second Zagreb index, Randić connectivity index, sum-connectivity index, Geometric-Arithmetic index and Atom-Bond Connectivity index of base-3 Sierpiński graphs are derived.
    VL  - 5
    IS  - 3
    ER  - 

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Author Information
  • School of Information Science and Engineering, Chengdu University, Chengdu, China

  • School of Information Science and Engineering, Chengdu University, Chengdu, China

  • Colleage of Pharmacy and Biological Engineering, Chengdu University, Chengdu, China

  • Department of Applied Mathematics of Iran University of Science and Technology, (IUST) Narmak, Tehran, Iran

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