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Revan Topological Indices of Quadrilateral Snake Graphs: Polynomial Formulations, Python Implementation, and Applications

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Bibliographic Details
Title: Revan Topological Indices of Quadrilateral Snake Graphs: Polynomial Formulations, Python Implementation, and Applications
Authors: Saranya, K M, Manimekalai, S
Source: The Nepali Mathematical Sciences Report; Vol. 42 No. 2 (2025); 162-177 ; 2392-411X
Publisher Information: Central Department of Mathematics, Tribhuvan University, Kathmandu, Nepal
Publication Year: 2025
Collection: Nepal Journals Online (NepJOL)
Subject Terms: Revan index, Quadrilateral snake graph, Python Program
Description: This study presents a detailed exploration of the Revan family of topological indices and their polynomial representations for diverse classes of quadrilateral snake graphs. Originating from the concept introduced by V. R. Kulli, Revan indices integrate both the minimum and maximum vertex degrees, which provide a refined measure of graph connectivity and structure. The research systematically derives explicit analytical expressions for Revan indices and their corresponding polynomials for four principal graph variants: standard, alternate, double, and cyclic quadrilateral snake graphs, highlighting their distinctive structural characteristics and degree-based relationships. To complement the theoretical formulations, a Python-based computational framework was developed to automate the calculation and symbolic representation of these indices. This implementation enables efficient validation of analytical results and facilitates the extension of Revan-based metrics to larger and more complex graph families. The findings underscore the potential of Revan indices as powerful structural descriptors in mathematical chemistry and network theory, with promising applications in quantitative modeling, cheminformatics, and the broader field of graph-based molecular design.
Document Type: article in journal/newspaper
File Description: application/pdf
Language: English
Relation: https://nepjol.info/index.php/nmsr/article/view/88560/67287; https://nepjol.info/index.php/nmsr/article/view/88560
Availability: https://nepjol.info/index.php/nmsr/article/view/88560
Accession Number: edsbas.4E901B1F
Database: BASE
Description
Abstract:This study presents a detailed exploration of the Revan family of topological indices and their polynomial representations for diverse classes of quadrilateral snake graphs. Originating from the concept introduced by V. R. Kulli, Revan indices integrate both the minimum and maximum vertex degrees, which provide a refined measure of graph connectivity and structure. The research systematically derives explicit analytical expressions for Revan indices and their corresponding polynomials for four principal graph variants: standard, alternate, double, and cyclic quadrilateral snake graphs, highlighting their distinctive structural characteristics and degree-based relationships. To complement the theoretical formulations, a Python-based computational framework was developed to automate the calculation and symbolic representation of these indices. This implementation enables efficient validation of analytical results and facilitates the extension of Revan-based metrics to larger and more complex graph families. The findings underscore the potential of Revan indices as powerful structural descriptors in mathematical chemistry and network theory, with promising applications in quantitative modeling, cheminformatics, and the broader field of graph-based molecular design.