On Eccentric Euler Sombor Index of a Graph

Habibi, Mohammad; Redžepović, Izudin; Rouhani, Soheir

doi:10.22049/cco.2026.30975.2686

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	On Eccentric Euler Sombor Index of a Graph
Communications in Combinatorics and Optimization
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 28 خرداد 1405 اصل مقاله (536.34 K)
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2026.30975.2686
نویسندگان
Mohammad Habibi¹؛ Izudin Redžepović^* ²؛ Soheir Rouhani¹^{، 3}
¹Department of Mathematics, Tafresh University, Tafresh 39518-79611, I. R. Iran
²Department of Natural Sciences and Mathematics, State University of Novi Pazar, Serbia
³Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran
چکیده
A novel vertex-degree-based topological index, namely the Euler Sombor index was defined as $ EU(G)=\sum\nolimits_{uv\in E(G)}{\sqrt{d_{u}^{2}+d_{v}^{2}+d_{u}d_{v}}}$. Based on this index, here we initiate the distance-based graph index as $\mathcal{E}_{ES}(G)=\sum\nolimits_{uv\in E(G)}{\sqrt{e^2(u)+e^2(v)+e(u)e(v)}}$ and call it the eccentric Euler Sombor index of a (chemical) graph $G = (V(G),E(G))$, where $e(u)$ and $e(v)$ are the eccentricity of $u$ and $v$ in $V(G)$, respectively. We establish basic mathematical properties of this new index. Also, we state some bounds for $\mathcal{E}_{ES}(G)$ in terms of order, size, degrees, radius, and diameter of $G$. We also determine trees (connected graphs, respectively) of a given order that have the minimum and maximum value of this index. Furthermore, we pose a conjecture about the maximum value of $\mathcal{E}_{ES}(G)$ when $G$ is a connected graph of fixed order.
کلیدواژه‌ها
eccentric Euler Sombor index؛ tree؛ graph invariants؛ eccentricity؛ distance

مراجع
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On Eccentric Euler Sombor Index of a Graph