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, I. R. Iran
تاریخ دریافت: 29 مرداد 1403، تاریخ پذیرش: 04 شهریور 1403
چکیده
Let G be a simple graph with vertex set V(G) = {v₁, v₂, …, v_n}. The elliptic Sombor matrix of G, denoted by A_ESO(G), is defined as the n × n matrix whose (i,j)-entry is (d_i+d_j)√(d_i²+d_j²) 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 ρ₁ ≥ ρ₂ ≥ … ≥ ρ_n which are the roots of the elliptic Sombor characteristic polynomial ∏_i=1ⁿ (ρ−ρ_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

مراجع
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Elliptic Sombor energy of a graph