Neighbors degree sum energy of commuting and non-commuting graphs for dihedral groups

• Main Authors: Romdhini, M. U., Nawawi, A., Chen, C. Y.
• Format: Article
• Language: English
• Published: Universiti Putra Malaysia 2023
• Online Access: http://psasir.upm.edu.my/id/eprint/108548/1/Neighbors%20Degree%20Sum%20Energy.pdf; http://psasir.upm.edu.my/id/eprint/108548/; https://mjms.upm.edu.my/lihatmakalah.php?kod=2023/March/17/1/53-65

The neighbors degree sum (NDS) energy of a graph is determined by the sum of its absolute eigenvalues from its corresponding neighbors degree sum matrix. The non-diagonal entries of NDS−matrix are the summation of the degree of two adjacent vertices, or it is zero for non-adjacent vertices, whereas for the diagonal entries are the negative of the square of vertex degree. This study presents the formulas of neighbors degree sum energies of commuting and non-commuting graphs for dihedral groups of order 2n, D2n, for two cases−odd and even n. The results in this paper comply with the well known fact that energy of a graph is neither an odd integer nor a square root of an odd integer.