‎For a graph $G$‎, ‎the exponential reduced Sombor index (ERSI)‎, ‎denoted by ${\\\\\\\\rm e}^{{\\\\\\\\rm SO}_{red}}$‎, ‎is $\\\\\\\\sum_{uv\\\\\\\\in\\\\\\\\,E(G)}{\\\\\\\\rm e}^{\\\\\\\\sqrt{(d_G(v)-1)^2+(d_G(u)-1)^2}}$‎, ‎where $d_G(v)$ is the degree of vertex $v$‎. ‎The authors in [On the reduced Sombor index and its applications‎. ‎MATCH Commun‎. ‎Math‎. ‎Comput‎. ‎Chem‎. ‎86 (2021) 729--753] conjectured that ‎for each ‎molecular tree ‎$‎T‎$‎ of order ‎$‎n‎$‎, ‎${\\\\\\\\rm e}^{{\\\\\\\\rm SO}_{red}}(T)\\\\\\\\leq \\\\\\\\frac{2}{3}(n+1){\\\\\\\\rm e}^3+\\\\\\\\frac{1}{3}(n-5){\\\\\\\\rm e}^{3\\\\\\\\sqrt{2}}$ where $n\\\\\\\\equiv2(\\\\\\\\mod 3)$‎, ‎${\\\\\\\\rm e}^{{\\\\\\\\rm SO}_{red}}(T)\\\\\\\\leq \\\\\\\\frac{1}{3}(2n+1){\\\\\\\\rm e}^3+\\\\\\\\frac{1}{3}(n-13){\\\\\\\\rm e}^{3\\\\\\\\sqrt{2}}+3{\\\\\\\\rm e}^{\\\\\\\\sqrt{13}}$ where $n\\\\\\\\equiv1(\\\\\\\\mod 3)$ and ${\\\\\\\\rm e}^{{\\\\\\\\rm SO}_{red}}(T)\\\\\\\\leq \\\\\\\\frac{2}{3}n{\\\\\\\\rm e}^3+\\\\\\\\frac{1}{3}(n-9){\\\\\\\\rm e}^{3\\\\\\\\sqrt{2}}+2{\\\\\\\\rm e}^{\\\\\\\\sqrt{10}}$ where $n\\\\\\\\equiv0(\\\\\\\\mod 3)$‎. ‎R‎ecently, Hamza and Ali [On a conjecture regarding the exponential reduced Sombor index of chemical trees. Discrete Math. Lett. 9 (2022) 107--110] proved the modified version of this conjecture. ‎In this paper‎, ‎we adopt another method to prove it.

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