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.
Topics
Graph theory
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