Neighbors Degree Sum Energy of Commuting and Non-Commuting Graphs for Dihedral Groups
Mamika Ujianita Romdhini, Athirah Nawawi, C.Y. Chen
Abstract
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.
Topics & Concepts
CombinatoricsDiagonalMathematicsDegree (music)Dihedral groupVertex (graph theory)Eigenvalues and eigenvectorsDihedral angleDegree matrixDiagonal matrixInteger (computer science)GraphDiscrete mathematicsGraph powerGroup (periodic table)PhysicsGeometryComputer scienceLine graphQuantum mechanicsProgramming languageAcousticsMoleculeHydrogen bondGraph theory and applicationsFinite Group Theory ResearchAdvanced Graph Theory Research