Elliptic Sombor energy of a graph

Alikhani, Saeid; Ghanbari, Nima; Dehghanizadeh, Mohammad Ali

doi:10.22061/jdma.2024.11190.1089

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	Elliptic Sombor energy of a graph
Journal of Discrete Mathematics and Its Applications
دوره 10، شماره 2، شهریور 2025، صفحه 143-155 اصل مقاله (348.44 K)
نوع مقاله: Full Length Article
شناسه دیجیتال (DOI): 10.22061/jdma.2024.11190.1089
نویسندگان
Saeid Alikhani^* ¹؛ Nima Ghanbari¹؛ Mohammad Ali Dehghanizadeh²
¹Department of Mathematical Sciences, Yazd University, 89195-741, Yazd, I. R. Iran
²Department of Mathematics, National University of Skills(NUS), Tehran, Iran
تاریخ دریافت: 29 مرداد 1403، تاریخ پذیرش: 04 شهریور 1403
چکیده
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.
کلیدواژه‌ها
elliptic Sombor matrix؛ elliptic Sombor energy؛ elliptic Sombor characteristic polynomial؛ eigenvalues؛ regular graphs

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Elliptic Sombor energy of a graph