Interested in molecular graph theory? This paper provides new inequalities relating several classes of variable topological indices, including general Zagreb indices, the general sum-connectivity index, and the variable inverse sum deg index. It seeks to establish upper and lower bounds for these indices in terms of molecular structural parameters. The research also explores upper and lower bounds on the inverse degree in terms of the first general Zagreb index. The characterization of extremal graphs with respect to many of these inequalities is obtained, providing a deeper understanding of the relationships between molecular structure and topological indices. Applications of these findings are also presented, demonstrating the practical utility of the developed inequalities in chemical graph theory and related fields.
As a publication in the Journal of Mathematical Chemistry, this article is consistent with the journal's emphasis on mathematical approaches to chemical problems. The development of new bounds for topological indices contributes to the theoretical foundation of chemical graph theory, a core area of interest for the journal's readership.