The elliptic Sombor energy of graphs

Articles in Press

Document Type : Original paper

Authors

1 Department of Mathematics, College of Science, University of Duhok, Duhok, Kurdistan Region,Iraq

2 Department of Mathematics, College of Basic Education, University of Duhok, Duhok, Kurdistan Region,Iraq

Abstract

The elliptic Sombor index is a topological index based on vertex degree introduced by  Gutman. Suppose $G=(V(G), E(G))$ is a finite, connected, and simple graph with  $V(G)=\{w_1, w_2, \dots, w_p\}$. Suppose $d_{G}(w_i)$ is
the degree of  $w_i$, for $1\leq i \leq p$. We use $ES(G)$ to represent the Sombor elliptic matrix $G$ which is  a
$p\times p$ matrix   and its $(i, j)$-entry is equal to $(d_{G}(w_{i})+d_{G}(w_{j}))\sqrt{d_{G}^{2}(w_{i})+d_{G}^{2}(w_{j})}$ if $w_{i}w_{j}\in E(G)$, and zero otherwise. We introduce and investigate the elliptic Sombor energy and elliptic Sombor
Estrada index, both base on the eigenvalues of the elliptic Sombor matrix. In addition, we prove some bounds for these new graph invariants.

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Main Subjects

References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 10 August 2025

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