geometric-quadratic index from a mathematical perspective

‎the geometric-quadratic index (gq) was defined in 2021 by v‎. ‎r‎. ‎kulli‎. ‎in a recent study‎, ‎qspr analysis for the octane isomers of gq and some other newly defined topological indices was presented‎. ‎this analysis has revealed that gq dominates over many of the well-known topological indices in terms of chemical applicability potential‎, ‎especially for the heat of vaporization‎. ‎these results inspired us to investigate the mathematical properties of gq‎. ‎in this paper‎, ‎extremal graphs for gq are investigated among connected graphs‎, ‎trees‎, ‎and unicyclic graphs‎. ‎in addition‎, ‎several mathematical relations between gq and some well-known topological indices are presented.