Sharp Bounds on the Generalized Multiplicative First Zagreb Index of Graphs with Application to QSPR Modeling

Degree sequence measurements on graphs have attracted a lot of research interest in recent decades. Multiplying the degrees adjacent vertices graph Ω provides multiplicative first Zagreb index graph. In context theory, generalized is defined as product sum αth powers vertex Ω, where α real number such that α≠0 and α≠1. The focus this work extremal for several classes including trees, unicyclic, bicyclic graphs, with respect to index. initial step, we identify set operations either increases or decreases graphs. We then involve analysis achieving sharp bounds by characterizing maximum minimum those classes. present applications Π1α predicting π-electronic energy Eπ(β) benzenoid hydrocarbons. particular, answer question concerning value which predictive potential Eπ lower hydrocarbons strongest. fact, our statistical delivers correlates correlation coefficient ρ=−0.998, if α=−0.00496. QSPR modeling, ρ=−0.998 considered be considerably significant.