LAPLACIAN AND SIGNLESS LAPLACIAN ENERGIES OF NON-COMMUTING GRAPH FOR GROUP U6n

The non-commuting graph on a group G, denoted by Gamma(G), has G\Z(G) as the vertex set and v(i), v(j) is an element of G\Z(G) are adjacent whenever v(i)v(j) not equal v(j)v(i). This research presented the Laplacian and signless Laplacian energies of Gamma G for group U6n, n >= 1. The result is that the two energies are of the same value and are always even integers. It is also found that Gamma(G) for U6n is hyperenergetic.