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This study addresses the limitations of conventional methods in dealing with dynamic molecular structures, focusing on the neighborhood M-polynomial (NM-polynomial), a pivotal polynomial for calculating degree-based TIs. Current literature acknowledges these polynomials but overlooks their limited adaptability to intricate biopolymer relationships. Our research advances by computing degree-based and neighborhood degree-based indices for prominent biopolymers, including polysaccharides, poly-<jats:inline-formula><a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><a:mi>\u03b3<\/a:mi><\/a:math><\/jats:inline-formula>-glutamic acid, and poly-L-lysine. Through innovative utilization of the NM-polynomial and the M-polynomial, we establish a fresh perspective on molecular structure and topological indices. Moreover, we present diverse graph representations highlighting the nuanced correlations between indices and structural parameters. By systematically investigating these indices and their underlying polynomials, our work contributes to predictive modelling in various fields. This exploration sheds light on intricate biochemical systems, offering insights into applications encompassing medicine, the food industry, and wastewater treatment. This research deepens our understanding of complex molecular interactions and paves the way for enhanced applications in diverse industries.<\/jats:p>","DOI":"10.1155\/2024\/1084450","type":"journal-article","created":{"date-parts":[[2024,2,2]],"date-time":"2024-02-02T23:35:12Z","timestamp":1706916912000},"page":"1-16","source":"Crossref","is-referenced-by-count":6,"title":["M-Polynomial and NM-Polynomial Methods for Topological Indices of Polymers"],"prefix":"10.1155","volume":"2024","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6316-7965","authenticated-orcid":true,"given":"Mohammed","family":"Yasin H","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur 603203, Tamil Nadu, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8842-6158","authenticated-orcid":true,"given":"M.","family":"Suresh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur 603203, Tamil Nadu, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0516-9211","authenticated-orcid":true,"given":"Zebene G.","family":"Tefera","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Addis Ababa University, Addis Ababa 1176, Ethiopia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6160-6485","authenticated-orcid":true,"given":"Samuel A.","family":"Fufa","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Addis Ababa University, Addis Ababa 1176, Ethiopia"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/j.molstruc.2022.133197"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1140\/epjp\/s13360-021-02074-8"},{"key":"3","first-page":"9372","article-title":"Neighborhood M-polynomial of crystallographic structures","volume":"11","author":"S. 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