On closed derivation formulas of the Nirmala indices from the M-polynomial of a graph |
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| Institution: | 1. Department of Chemistry, Mashhad Branch, Islamic Azad University, Mashhad, Iran;2. Department of Chemistry, Quchan Branch, Islamic Azad University, Quchan, Iran;1. PG and Research Department of Chemistry, Sri Sarada College for Women (Autonomous), Salem, 636016, Tamil Nadu, India;2. Department of Chemistry, Chikkaiah Naicker College, Erode, 638 004, Tamil Nadu, India;1. Deputy for Research and Innovation Infrastructure, National Research and Innovation Agency, Jl. Babarsari Postal Code 6101 ykbb, Yogyakarta, 55281, Indonesia;2. Research Center for Mining Technology, National Research and Innovation Agency, Kawasan Sains Tanjung Bintang Jl. Sutami KM 15, Tanjung Bintang, Lampung Selatan, 35361, Indonesia |
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| Abstract: | A new category of polymeric materials is dendrimers. These are monodisperse macromolecules with a high branching level. The physical and chemical characteristics of these materials are strongly influenced by their structure. Dendrimers are ideal for a wide variety of biological and industrial applications due to their distinctive behaviour. Very recently, in 2021, the Nirmala index, and the first and second inverse Nirmala indices are proposed and calculated their values for four standard dendrimers. In this present article, we propose closed derivation formulas for finding the above variations of Nirmala indices of a graph in terms of its M-polynomial. We also determine the M-polynomials and their geometrical natures for some families of dendrimers. Finally, we compute the Nirmala indices for each of the considered dendrimers using the M-polynomial approach based on the proposed closed derivation formulas and get the same numeric results as originally calculated. |
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| Keywords: | Nirmala indices Degree-based topological index M-polynomial Dendrimers Graph polynomial 05C10 05C07 92E10 05C31 |
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