Malaysian Journal of Mathematical Sciences, March 2024, Vol. 18, No. 1

Some New Bounds on the Modified Symmetric Division Deg Index

Gowtham, K. J., Husin, M. N., and Siddiqui, M. K.

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Received date: 8 October 2023
Accepted date: 8 November 2023

The use of graph theory in the fields of chemistry, pharmacy, communication, maps, and aeronautics is significant. In order to study the properties of chemical compounds, the molecules of those compounds are modeled as graphs. Boiling point, enthalpy, $\pi$-electron energy, and molecular weight are a few examples of physical properties that are related to the geometric structure of the compound. Recently, the modified symmetric division deg (${}^mSDD(\mathcal{G})$, in short) index is {defined} as the total of all adjacent vertices in pairs $\mu \upsilon$ of the term $\sqrt{\dfrac{1}{2}\left(\dfrac{d_\mu}{d_\nu}+\dfrac{ d_\nu}{d_\mu} \right)}$. The purpose of this article is to demonstrate the usefulness of ${}^mSDD(\mathcal{G})$ index through the resolution of an interdisciplinary problem describing the structure of benzenoid hydrocarbons. With the help of linear regression models, we have studied the physicochemical properties of benzenoid hydrocarbons. Strong correlations were obtained, and the bounds for the same index were subsequently established.

Keywords: topological inidces; modified symmetric division deg index; graph



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