On Spectrum and Energy of Non-Commuting Graph for Group U_6n - Romdhini, Mamika Ujianita; Nawawi, Athirah; Al-Sharqi, Faisal; Al-Quran, Ashraf (IndoMS, 2025)
Let G be a group and Z(G) be the center of G. In this paper, we discuss a specific type of graph known as the non-commuting graph, denoted by Γ_G, whose vertex set contains all group elements excluding central elements, GZ(G). This graph has to satisfy a condition in which v_p,v_q GZ(G) where v_p ≠ v_q, are adjacent whenever v_p v_q≠ v_q v_p. This paper presents the spectrum and energy of the non-commuting graph for U_6n, Γ_U_6n associated with the adjacency, degree sum, and degree sum adjacency matrices and their energy relationship.