In this paper, we examine the Gutman-Milovanovic index and establish new upper and lower bounds for it. These bounds include terms related to the general sum connectivity index, the general second Zagreb index, and the hyperbolicity constant of the underlying graph. Also, we model physicochemical properties of polyaromatic hydrocarbons using the Gutman-Milovanovic index.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.. The research of third author (Y.Q.) has been partially supported by Grant CEX2019-000904-S, funded by: MCIN/AEI/10.13039/501100011033
