Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 Articles in Press 2026 01 29 Analytical Study of Second Inverse Sum Indeg Index of Special Graphs 15098 10.22049/cco.2026.31269.2801 EN Mohamadreza Rostami Faculty of science, Mahallat Institute of Higher Education, Mahallat, Iran Dariush Heidari Faculty of science, Mahallat Institute of Higher Education, Mahallat, Iran Ivan Gutman Faculty of Science, University of Kragujevac, Kragujevac, Serbia Liju Alex Department of Applied Science( Mathematics), Rajiv Gandhi Institute of Technology (RIT), Kottayam – 686501, India Journal Article 2025 11 30 In this paper, we investigate the second inverse sum indeg index $ISI_2$ of graphs, a topological index that has significant applications in chemical graph theory. Upper and lower bounds for $ISI_2$ of graphs and trees with a specified number of pendent edges are established. Furthermore, $ISI_2$ of various bridge graphs are computed. The main contribution of this work lies in presenting precise bounds and exact expressions for particular families of graphs, offering resources for researchers and engineers in mathematical chemistry and applied graph theory. topological index second inverse sum indeg index bridge graph https://comb-opt.azaruniv.ac.ir/article_15098_bd2fb114233f043f2754c59690c0b244.pdf