Seidel energy of non-commuting graph for the group U6n

Abstract

The non-commuting graph for the group G, denoted by ΓG, whose vertex set contains all group elements excluding central elements, where two distinct vertices vi and vj are adjacent whenever vivj ≠ vjvi. The non-diagonal entries of the Seidel matrix are −1 for two adjacent vertices, or one for non-adjacent vertices, whereas the diagonal entries are zero. This study presents the spectrum and energy of ΓG for the group G = U6n associated with the Seidel matrix.