Document Type : Research Paper
Department of Applied Mathematics, Faculty of Mathematical Sciences Ferdowsi University of Mashhad P.O. Box 1159, Mashhad 91775, Iran
For a graph G, the exponential reduced Sombor index (ERSI), denoted by eSored , is ∑uv∈E(G) e√(dG(v)-1)^2+(dG(u)-1)^2), where dG(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, eSored(T)≤(2/3) (n+1) e3 +(1/3) (n-5) e 3√2, where n≡2 (mod 3), eSored(T)≤(1/3) (2n+1) e3 +(1/3) (n-13) e3√2 + 3e√13 , where n≡1 (mod 3) and eSored(T)≤(2/3) ne3 +(1/3) (n-9) e3√2 + 2e√10 , where n≡0 (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.