Abstract
Let 𝑛 be positive integer and 𝑊𝑛 be a wheel graph of order 𝑛. In this paper, we construct a new decomposition of 8𝐾𝑣 into wheel graphs for 𝑣 ≡ 2 (mod 12). Then, new cyclic triple system will be defined to arrange 𝑣 × 2(𝑣 − 1) triples satisfying certain criteria. In this development, the decomposition of 8𝐾𝑣 will be used to construct a cyclic 12-fold triple system of order 𝑣 ≡ 2 (mod 12).
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