Abstract

What distinguishes entire topological indices from other topological indices is that their formulas include information about both the edges and vertices, not just the connections between vertices. This provides more comprehensive and detailed picture of the graph’s structure. In our article, we study and analyze some entire Zagreb indices by investigating their behavior for four families of graphs; subdivision graphs, central graphs, corona products and m bridge graphs over path, cycle and complete graphs. We explore the properties of these graph structures by deriving explicit formulae for the first, second and modified first entire Zagreb indices for each family. Our results provide detailed information on the structural properties stored by the first, second and modified entire Zagreb indices. These different graph families show the way for future research and potential applications in fields such as chemical modeling and network investigation.

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