Decompositions of Complete Multigraphs into Cyclic Designs

Abstract

Let and be positive integer, denote a complete multigraph. A decomposition of a graph is a set of subgraphs of whose edge sets partition the edge set of . The aim of this paper, is to decompose a complete multigraph into cyclic -cycle system according to specified conditions. As the main consequence, construction of decomposition of into cyclic Hamiltonian wheel system, where , is also given. The difference set method is used to construct the desired designs.

Keywords

• cyclic design
• hamiltonian cycle
• near four factor
• wheel graph.