University of Isfahan Transactions on Combinatorics 2251-8657 10 2 2021 06 01 Exponential second Zagreb index of chemical trees 97 106 25094 10.22108/toc.2020.125047.1764 EN Selvaraj Balachandran Department of Mathematics and Applied Mathematics, University of the Free State, P. O. Box 339, Bloemfontein, 9300, South Africa Tomas Vetrik Department of Mathematics and Applied Mathematics, University of the Free State, P. O. Box 339, Bloemfontein, 9300, South Africa Journal Article 2020 09 22 ‎Cruz‎, ‎Monsalve and Rada [Extremal values of vertex-degree-based topological indices of chemical trees‎, ‎Appl‎. ‎Math‎. ‎Comput‎. ‎380 (2020) 125281] posed an open problem to find the maximum value of the exponential second Zagreb index for chemical trees of given order‎. ‎In this paper‎, ‎we solve the open problem completely‎. https://toc.ui.ac.ir/article_25094_5298fdaa10ea354bf8e85a8d5bef55de.pdf