Abstract
Let v and λ be positive integer, λKv denote a complete multigraph. A decomposition of a graph G is a set of subgraphs of G whose edge sets partition the edge set of G. In this article, difference set method is used to introduce a new design that is decomposed a complete multigraph into near Hamiltonian cycles. In course of developing this design, a combination between near-4-factor and a cyclic (v − 1)-cycle system of 4Kv, when v = 4n + 2, n > 2, will be constructed.
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