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Mathematics and Statistics Vol. 13(4), pp. 181 - 193
DOI: 10.13189/ms.2025.130401
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Investigating the Use of M-Polynomial for Calculating Topological Indices in Carbazole Dendrimers

A. Venkatesan ¹, R. Binthiya ², B. Roopa ², A. Jeslet Kani Bala ^2,*
1 PG & Research Department of Mathematics, St. Joseph's College of Arts & Science (Autonomous), Cuddalore-607001, Tamil Nadu, India
² SRM Institute of Science and Technology, Ramapuram, Chennai, Tamil Nadu, India

ABSTRACT

Graph theory plays an essential role in analysing the structural characteristics of molecular structures and network systems. Among the various degree-based topological indices, the Hyper Zagreb index, Redefined Zagreb index, and Reciprocal Randic index are particularly important for evaluating molecular graphs. I investigated the M-polynomial as a tool for calculating the Hyper Zagreb index, Redefined Zagreb index, and Reciprocal Randic index. Carbazole dendrimers are highly branched macromolecular structures consisting of a central carbazole unit with multiple dendritic branches extending from it. We successfully determined the M-polynomials for Carbozole dendrimers. Furthermore, by leveraging these M-polynomials, we will be computing various topological indices based on degree. Additionally, we obtained the Topological Indices values of Carbozole dendrimers for generations using the M-polynomial. The M-polynomial is firstly used and is determined as follows: . Where and is the total number of edges , where . The theory of Quantitative Structure-Property Relationships (QSPR) is founded on the principle that a compound's physicochemical properties are intrinsically linked to its molecular structure. The results of this study provide a thorough framework for examining dendritic structures using M-polynomials, which adds to the expanding collection of work on molecular graph theory. These findings might help develop prediction models for quantitative structure鈥損roperty relationship (QSPR) research, especially when it comes to comprehending the physiochemical characteristics of dendritic molecules.

KEYWORDS
Topological Indices, M-Polynomial, Carbozole Dendrimers

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] A. Venkatesan , R. Binthiya , B. Roopa , A. Jeslet Kani Bala , "Investigating the Use of M-Polynomial for Calculating Topological Indices in Carbazole Dendrimers," Mathematics and Statistics, Vol. 13, No. 4, pp. 181 - 193, 2025. DOI: 10.13189/ms.2025.130401.

(b). APA Format:
A. Venkatesan , R. Binthiya , B. Roopa , A. Jeslet Kani Bala (2025). Investigating the Use of M-Polynomial for Calculating Topological Indices in Carbazole Dendrimers. Mathematics and Statistics, 13(4), 181 - 193. DOI: 10.13189/ms.2025.130401.