University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 17 2 2026 06 01 New Results on Second Inverse Sum Indeg Index 113 128 115558 10.22052/ijmc.2025.257454.2055 EN Dariush Heidari Faculty of science‎, ‎Mahallat Institute of Higher Education‎, ‎Mahallat‎, ‎Iran Mohamadreza Rostami Faculty of science‎, ‎Mahallat Institute of Higher Education‎, ‎Mahallat‎, ‎Iran Ivan Gutman Faculty of Science‎, ‎University of Kragujevac‎, ‎Kragujevac‎, ‎Serbia Liju Alex Bishop Chulaparambil Memorial College‎, ‎Kottayam-686001‎, ‎India Journal Article 2025 08 19 ‎The second inverse sum indeg topological index $(ISI_2)$ is considered as a valuable tool for the study of graphs and trees‎. This index is systematically investigated‎ for the first time‎, ‎and its upper and lower bounds are derived for general graphs and trees‎. ‎Furthermore‎, ‎comparisons between $ISI_2$ and other existing topological indices are presented‎. The results demonstrate that $ISI_2$ not only provides valuable insights into‎ the structure of graphs but also serves as a powerful instrument for modeling and‎ ‎analyzing complex networks‎, ‎particularly in chemistry and pharmacology‎. Specifically‎, ‎$ISI_2$ exhibits significant potential in predicting physicochemical‎ properties of molecules‎, ‎such as polarity‎, ‎boiling point‎, ‎and biological activity‎. ‎Thus‎, $ISI_2$ may serve for the design and optimization of novel drug molecules and chemical compounds‎. https://ijmc.kashanu.ac.ir/article_115558_f4ae081b9d19512aad6a751a44c19dff.pdf