A Novel Relationship Between Well-Known Indices: Sombor, Mostar, and Zagreb Indices

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Abstract
Graph descriptors such as normalized Laplacian energy, Sombor index, Mostar index and Zagreb index are often employed in various scientific contexts. The Sombor index is essential in chemical graph theory because it provides insights into molecule stability and reactivity by analyzing the distribution of atom degrees and distances. By measuring molecular graph topology, the Zagreb indices are vital tools in mathematical chemistry that help predict molecules’ physical and chemical characteristics. This manuscript aims to broaden the characterization of extremal graphs, achieving upper sharp bounds for the Mostar and first Zagreb index with given parameters such as cut edges and girth.

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