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Mathematics 2019, 7(3), 271;

On Irregularity Measures of Some Dendrimers Structures

School of Information Science and Technology, Yunnan Normal University, Kunming 650500, China
Faculty of Physical and Numerical Sciences, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
School of Natural Sciences, National University of Sciences and Technology, Sector H-12, Islamabad 44000, Pakistan
Department of Natural Sciences and Humanities, University of Engineering and Technology, Lahore(RCET) 54000, Pakistan
Author to whom correspondence should be addressed.
Received: 30 January 2019 / Revised: 7 March 2019 / Accepted: 13 March 2019 / Published: 16 March 2019
PDF [354 KB, uploaded 16 March 2019]


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.
Keywords: irregularity index; molecular graph; dendrimers irregularity index; molecular graph; dendrimers
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Gao, W.; Aamir, M.; Iqbal, Z.; Ishaq, M.; Aslam, A. On Irregularity Measures of Some Dendrimers Structures. Mathematics 2019, 7, 271.

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