Exploring second Zagreb and neighborhood first Zagreb indices in (γ,ρ)-generalized transformation graphs: A dual-index approach to network analysis

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In graph theory, the study of transformation graphs has recently expanded to include generalized versions enabling the modeling and analysis of infinite number of graphs, offering new insights into network analysis. By transforming graphs into more complex versions while retaining the core structure of the original, we unlock enhanced applications and insights across various domains, all rooted in the foundational properties of the primary graph. This paper presents an innovative approach to explore graph properties through the calculation of second Zagreb index and neighborhood first Zagreb index using neighborhood Degree in [Formula: see text]-Generalized Transformation graphs. This approach enhances accuracy and provides deeper insights into graph structures, making it particularly relevant for applications in network analysis, social media, biological systems, and extensive data analytics. This dual-index approach marks a significant leap in graph theory, providing a robust framework for future explorations and applications in complex networks.