Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 Articles in Press 2025 06 11 Max-min degree index of a graph and it’s mathematical relation with other topological indices 14969 10.22049/cco.2025.30390.2450 EN Shibsankar Das Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India 0000-0003-0082-6673 Biswaranjan Khanra Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India Journal Article 2025 03 04 Among the defined $148$ discrete Adriatic indices, the max-min degree index is one. Vuki{\'c}evi\'c proposed some problems related to the upper and lower bounds on the max-min degree index. Here we determine the max-min degree index of some special graphs. We characterize the graphs extremal with respect to max-min degree index over connected graphs, trees and unicyclic graphs with a given number of vertices. Finally, we establish its mathematical relation with other topological indices. tree Unicyclic graph Bound https://comb-opt.azaruniv.ac.ir/article_14969_354608713e12a485ff9b05ff90dc9028.pdf