Optimizing the Euler-Sombor Index of (Molecular) Tricyclic Graphs

Let G be a graph with edge set E(G). Denote by d(u) the degree of a vertex u in G. The Euler-Sombor index of G is defined as (Figure Presented). A graph with a maximum degree not more than 4 is known as a molecular graph. By a tricyclic graph of order n, we mean a connected graph of order n and size n + 2. This paper demonstrates that both the main results of the recent paper [G. O. Kızılırmak, MATCH Commun. Math. Comput. Chem. 94 (2025) 247–262] can be obtained by using the known results. The graphs attaining the optimal values of the Euler-Sombor index among all molecular tricyclic graphs of a given order are also reported.