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.
Alikhani, S. , Ghanbari, N. and Dehghanizadeh, M. A. (2025). Elliptic Sombor energy of a graph. Journal of Discrete Mathematics and Its Applications, 10(2), 143-155. doi: 10.22061/jdma.2024.11190.1089
MLA
Alikhani, S. , , Ghanbari, N. , and Dehghanizadeh, M. A. . "Elliptic Sombor energy of a graph", Journal of Discrete Mathematics and Its Applications, 10, 2, 2025, 143-155. doi: 10.22061/jdma.2024.11190.1089
HARVARD
Alikhani, S., Ghanbari, N., Dehghanizadeh, M. A. (2025). 'Elliptic Sombor energy of a graph', Journal of Discrete Mathematics and Its Applications, 10(2), pp. 143-155. doi: 10.22061/jdma.2024.11190.1089
CHICAGO
S. Alikhani , N. Ghanbari and M. A. Dehghanizadeh, "Elliptic Sombor energy of a graph," Journal of Discrete Mathematics and Its Applications, 10 2 (2025): 143-155, doi: 10.22061/jdma.2024.11190.1089
VANCOUVER
Alikhani, S., Ghanbari, N., Dehghanizadeh, M. A. Elliptic Sombor energy of a graph. Journal of Discrete Mathematics and Its Applications, 2025; 10(2): 143-155. doi: 10.22061/jdma.2024.11190.1089
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