Maple computations on the energy of cayley graphs for dihedral groups

Abstract

Maple software is very useful in assisting various types of mathematical computations. The software provides many packages that can be explored such as Group Theory package, Graph Theory package and Linear Algebra package. The group theory package provides a collection of commands for computing and visualizing finitely generated groups. Meanwhile, the Graph Theory package is a collection of commands for creating graphs, drawing graphs, manipulating graphs and testing graphs for certain properties. The graphs are consists of sets of vertices which are connected by edges. The package supports both directed and undirected graphs but in this research, only undirected graphs are being considered. The aim of this paper is to present the Maple computation of the energy of Cayley graphs for a subset of the dihedral groups. The computation includes the construction of the Cayley graphs followed by the formation of their adjacency matrix and the computation of their eigenvalues. Lastly, the energy of the Cayley graphs can be found by calculating the summation of the absolute values of the eigenvalues found.