The first and second Zagreb indices of a hypergraph

In QSAR and QSPR analyses, topological indices of a graph refer to numerical descriptors derived from the connectivity patterns of atoms in a molecular structure. Representing molecules using molecular graphs involves creating a visual or mathematical representation where atoms are represented as nodes, and chemical bonds as edges, providing a structured framework to analyze molecular structure and properties. However, in order to model the compounds, where there exists a delocalized polycentric bonds, graphs may not be the proper tool, where these compounds can be modeled through hypergraphs. A hypergraph is said to be a uniform hypergraph, if every hyperedge in the hypergraph contains the same number of vertices. A minimally connected hypergraph is a hypergraph, where the removal of any hyperedge disconnects the hypergraph. In this paper, we have given the bounds for the first and second Zagreb indices of general and bipartite hypergraphs. The extremal hypergraphs in the family of minimally connected hypergraphs corresponding to the first and second Zagreb indices have been obtained. Additionally, we have proposed a new hypergraph representation for hydrocarbons and determined the extent of correlation between the physicochemical characteristics of octane isomers and the Zagreb and Sombor indices of these molecular hypergraphs. This study also supports SDG 4 (Quality Education) by advancing tools that can enhance the learning and understanding of computational techniques, molecular structures and its properties in educational settings.