SEIDEL ENERGY OF NON-COMMUTING GRAPH FOR THE GROUP U6n

SEIDEL ENERGY OF NON-COMMUTING GRAPH FOR THE GROUP U6n

M. U. Romdhini , A. Nawawi , F. Al-Sharqi , A. Al-Quran

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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.

Keywords

Seidel matrix, energy of a graph, non-commuting graph, U6n.