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Title:
Optimizing the Euler-Sombor Index of (Molecular) Tricyclic Graphs
Authors:
Abeer M. Albalahi, Abdulaziz M. Alanazi, Abdulaziz Mutlaq Alotaibi, Amjad E. Hamza, Akbar Ali
Volume
94
Issue
2
Year
2025
Pages
549-560
Abstract

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 \( EU(G) = \sum_{uv\in E(G)} \sqrt{(d(u)+d(v))^2 - d(u)\, d(v)} \). 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.