Decomposition Hamilton in Cayley Graphs with Certain Invers Generator of Dihedral-$$2n$$ Group

Abstract

The Hamilton decomposition of graph G is a partition of the edge set into a Hamilton cycle and 1-factor if the vertex degree is odd or a partition into a Hamilton cycle if the degree of the vertex is even. In 2020, the focus was on determining the Hamilton decomposition of a Cayley graph in the dihedral-2p group, where p is a single prime. In this paper, the Hamiltonian decomposition of the Cayley graph will be determined from the dihedral-2n group, with n ≥ 3. This research aims to determine Hamiltonian decomposition, which focuses on generating {r n−1 , s} from dihedral groups. The research method is to determine the dihedral-2n group, determine the set of vertices and the set of edges of the Cayley graph, construct the Cayley graph generated by {r n−1 , s}, and decompose the Cayley graph using Hamiltonian. The vertex degree of the Cayley graph, constructed by the dihedral-2n group and generated by {r n−1 , s}, , is an odd vertex. Graph decomposition results are a Hamilton cycle and 1-factor (perfect matching).