Closeness Energy of Non-Commuting Graph for Dihedral Groups
Keywords:Closeness matrix, Energy of a graph, Non-commuting graph, Dihedral Groups
This paper focuses on the non-commuting graph for dihedral groups of order 2n, D2n, where n ≥ 3. We show the spectrum and energy of the graph corresponding to the closeness matrix. The result is that the obtained energy is always twice its spectral radius and is never an odd integer. Moreover, it is classified as hypoenergetic.
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