Let K_n denote the complete graph of n vertices. Let C_(24) be the 24-cycle. The C_(24)-t-foil is a graph of t edge-disjoint C_(24)'s with a common vertex and the common vertex is called the center of the C_(24)-t-foil In particular, the C_(24)-2-foil and the C_(24)-3-foil are called the C_(24)-bowtie and the C_(24)-trefoil, respectively. When K_n is decomposed into edge-disjoint sum of C_(24)-t-foils, it is called that K_n has a C_(24)-t-foil decomposition. Moreover, when every vertex of K_n appears in the same number of C_(24)-t-foils， it is called that K_n has a balanced C_(24)-t-foil decomposition and this number is called the replication number.
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