We investigate the uniqueness of factorisation of possibly disconnectedfinite graphs with respect to the Cartesian, the strong and the direct product.It is proved that if a graph has $n$ connected components, where $n$ is prime,or $n=1,4,8,9$, and satisfies some additional conditions, it factors uniquelyunder the given products. If, on the contrary, $n=6$ or 10, all cases ofnonunique factorisation are described precisely.
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机译：我们研究了关于笛卡尔，强和直接乘积的可能不连续有限图的因式分解的唯一性，证明了如果一个图具有$ n $个连通分量，其中$ n $是素数，或$ n = 1， 4,8,9 $，并且满足一些其他条件，它在给定产品下是唯一的因素。相反，如果n = 6或10，则精确描述所有非唯一因式分解的情况。
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