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Title:
On the Degree‑Ratio Sombor Index and Graph Energy
Authors:
Zhonglin Cheng ORCID iD 0000-0003-2306-9556
Xiaoye Ding ORCID iD 0000-0001-5318-3507
ChunJie Wu
Jiang Houting
Huiqin Chu ORCID iD 0009-0002-9006-5416
Volume
97
Issue
3
Year
2027
Pages
1251-1261
Abstract

The energy of a simple graph \(G\) is defined as the sum of absolute values of all eigenvalues of its adjacency matrix and is denoted by \(\mathcal{E}(G)\). The Degree‑Ratio Sombor index of \(G\) is defined as \[ \operatorname{DRSO}(G)=\sum_{uv\in E(G)}\frac{\sqrt{d_u^{4}+d_v^{4}}}{d_u d_v}, \] where \(d_u\) and \(d_v\) are the degrees of vertices \(u\) and \(v\), respectively. In this paper, we investigate the relationship between \(\operatorname{DRSO}(G)\) and \(\mathcal{E}(G)\).