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On Irregularity Measures of Some Dendrimers Structures

Author

Listed:
  • Wei Gao

    (School of Information Science and Technology, Yunnan Normal University, Kunming 650500, China)

  • Muhammad Aamir

    (Faculty of Physical and Numerical Sciences, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan)

  • Zahid Iqbal

    (School of Natural Sciences, National University of Sciences and Technology, Sector H-12, Islamabad 44000, Pakistan)

  • Muhammad Ishaq

    (School of Natural Sciences, National University of Sciences and Technology, Sector H-12, Islamabad 44000, Pakistan)

  • Adnan Aslam

    (Department of Natural Sciences and Humanities, University of Engineering and Technology, Lahore(RCET) 54000, Pakistan)

Abstract

A graph is said to be a regular graph if all its vertices have the same degree, otherwise, it is irregular. Irregularity indices are usually used for quantitative characterization of the topological structure of non-regular graphs. In numerous applications and problems in material engineering and chemistry, it is useful to be aware that how irregular a molecular structure is? Furthermore, evaluations of the irregularity of underline molecular graphs could be valuable for QSAR/QSPR studies, and for the expressive determines of chemical and physical properties, such as enthalpy of vaporization, toxicity, resistance, Entropy, melting and boiling points. In this paper, we think over the following four irregularity measures: the irregularity index by Albertson, σ irregularity index, the total irregularity index and the variance of vertex degrees. By way of graph structural estimation and derivations, we determine these irregularity measures of the molecular graphs of different classes of dendrimers.

Suggested Citation

  • Wei Gao & Muhammad Aamir & Zahid Iqbal & Muhammad Ishaq & Adnan Aslam, 2019. "On Irregularity Measures of Some Dendrimers Structures," Mathematics, MDPI, vol. 7(3), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:271-:d:214482
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    References listed on IDEAS

    as
    1. Gutman, Ivan, 2018. "Stepwise irregular graphs," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 234-238.
    2. Chen, Xiaodan & Hou, Yaoping & Lin, Fenggen, 2018. "Some new spectral bounds for graph irregularity," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 331-340.
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    Cited by:

    1. Martin Kenyeres & Jozef Kenyeres, 2023. "Distributed Average Consensus Algorithms in d-Regular Bipartite Graphs: Comparative Study," Future Internet, MDPI, vol. 15(5), pages 1-24, May.

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