Elliptic Sombor energy of a graph

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Alikhani Saeid; Ghanbari Nima; Dehghanizadeh Mohammad Ali

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Journal Paper

Paper Information

Journal: Journal of Discrete Mathematics and its Applications Year:2025 | Volume:10 | Issue:2 Page(s): 143-155

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Information Journal Paper

Title

Elliptic Sombor energy of a graph

Author(s)

Alikhani Saeid | Ghanbari Nima | Dehghanizadeh Mohammad Ali | Issue Writer Certificate

Keywords

Elliptic Sombor Matrix

Elliptic Sombor Energy

Elliptic Sombor Characteristic Polynomial

Eigenvalues

Regular Graphs

Abstract

Let $G$ be a simple graph with vertex set $V(G) = \{v_1, v_2,\ldots, v_n\}$. The Elliptic Sombor Matrix of $G$, denoted by $A_{ESO}(G)$, is defined as the $n\times n$ matrix whose $(i,j)$-entry is $(d_i+d_j)\sqrt{d_i^2+d_j^2}$ if $v_i$ and $v_j$ are adjacent and $0$ for another cases.Let the Eigenvalues of the Elliptic Sombor Matrix $A_{ESO}(G)$ be $\rho_1\geq \rho_2\geq \ldots\geq \rho_n$ which are the roots of the Elliptic Sombor Characteristic Polynomial $\prod_{i=1}^n (\rho-\rho_i)$. The Elliptic Sombor Energy ${E_{ESO}}$ of $G$ is the sum of absolute values of the Eigenvalues of $A_{ESO}(G)$. In this paper, we compute the Elliptic Sombor Characteristic Polynomial and the Elliptic Sombor Energy for some graph classes. We compute the Elliptic Sombor Energy of cubic graphs of order $10$ and as a consequence, we see that two $k$-regular graphs of the same order may have different Elliptic Sombor Energy.

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