On Eccentric Euler Sombor Index of a Graph

Articles in Press

Document Type : Original paper

Authors

1 Department of Mathematics, Tafresh University, Tafresh 39518-79611, I. R. Iran

2 Department of Natural Sciences and Mathematics, State University of Novi Pazar, Serbia

3 Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran

Abstract

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.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 18 June 2026

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