Astri Kumala, Hery Susanto, Desi Rahmadani
A decomposition of a graph G is a collection of edge-disjoint subgraphs H1, H2, ..., Hr of G such that every edge of G belongs to exactly one Hi. In 2020, Hamiltonian decomposition of Cayley graphs in the dihedral-2p group, where p is a single prime have been studied. In this paper, we study the Hamiltonian decomposition of a Cayley graph of the dihedral-2n group with n ≥ 3. We determine the Hamilton decomposition of the Cayley graphs of a dihedral group on the certain generator {r, r-1, s} of a dihedral group. We show that the Cayley graphs can be decomposed into a Hamiltonian cycle and perfect matching. © 2024 Author(s).
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Malang, Malang, Indonesia
