On spectrum and energy of non-commuting graph for group U6n - Romdhini, Mamika Ujianita; Nawawi, Athirah; Al-Sharqi, Faisal; Al-Quran, Ashraf (The Indonesian Mathematical Society, 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 ΓG, whose vertex set contains all group elements excluding central elements, G\Z(G). This graph has to satisfy a condition in which vp, vq ∈ G\Z(G) where vp ≠ vq, are adjacent whenever vpvq ≠ vqvp. This paper presents the spectrum and energy of the non-commuting graph for U6n, ΓU6n associated with the adjacency, degree sum, and degree sum adjacency matrices and their energy relationship.