Maximum and minimum degree energy of commuting graph for dihedral groups

If is a finite group and is the centre of , then the commuting graph for , denoted by , has as its vertices set with two distinct vertices and are adjacent if . The degree of the vertex of , denoted by , is the number of vertices adjacent to . The maximum (or minimum) degree matrix of is a square matrix whose -th entry is whenever and are adjacent, otherwise, it is zero. This study presents the maximum and minimum degree energies of for dihedral groups of order , by using the absolute eigenvalues of the corresponding maximum degree matrices ( ) and minimum degree matrices ( ).Here, the comparison of maximum and minimum degree energy of for is discussed by considering odd and even cases. The result shows that for each case, both energies are non-negative even integers and always equal.

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