Seidel energy for Cayley graphs associated to dihedral group

Abstract

The studies on the energy of a graph have been actively studied since 1978 and there have been various types of energy of graphs proposed and studied by mathematicians all over the world. One of the many types of energy being studied is Seidel energy, where it is defined as the summation of the absolute values of the eigenvalues of the Seidel matrix of a graph. This research combines the study on three important branches in mathematics, i.e. energy of graph in linear algebra, Cayley graph in graph theory and dihedral group in group theory. The aim of this research is to present some values of Seidel energy of Cayley graphs associated to dihedral groups with respect to certain subsets of the group, namely the subsets of order one and the subsets of order two; {a, a n–1} for n ≥ 3 and {a 2, a n–2} for n ≥ 5. The results are proven by using some properties of special graphs such as complete graph, cycle graph and complete bipartite graph, including some relations between the eigenvalues of a graph, with the Seidel eigenvalues of a graph.