| Summary: | In this paper, we solved some open problems on general Gutman index. More precisely, we characterized unicyclic graphs with extremal general Gutman index for some $ a $ and $ b $. We presented a sharp bound on general Gutman index of $ G $ in terms of order and vertex connectivity of $ G $. Also, we obtained some bounds on general Gutman index in terms of order, general Randić index, diameter, and independence number of graph $ G $. In addition, QSPR analysis on various anticancer drug structures was carried out to relate their physicochemical properties with the general Gutman index of the structure for some $ a $ and $ b $.
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