In 1983, D. Marusic initiated the determination of the set NC of non-Cayley numbers. A number n belongs to NC if there exists a vertex-transitive, non-Cayley graph of order n. The status of all non-square-free numbers and the case when n is the product of two primes was settled recently by B. D. McKay and C. E. Praeger. Here we deal with the smallest unsolved case, when n is the product of three distinct odd primes. We list a set of numbers n of this form which belong to NC. We also show that if there exists a vertex-primitive or quasiprimitive non-Cayley graph of order n = pqr then the number n occurs on our list. Moreover, we conjecture that the list we compiled contains all non-Cayley numbers of the form n = pqr.
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机译：1983年，D。Marusic发起了对非凯伊数的集合NC的确定。如果存在阶数为n的顶点可传递的非凯利图，则数字n属于NC。 B. D. McKay和C. E. Praeger最近解决了所有非平方无数的状态以及n是两个素数的乘积的情况。在这里，我们处理最小的未解决情况，即n是三个不同奇数素数的乘积。我们列出了属于NC的一组这种形式的数字n。我们还表明，如果存在阶为n = pqr的顶点本原或准本原非凯伊图，则数字n出现在我们的列表中。此外，我们推测我们编译的列表包含形式为n = pqr的所有非凯伊数。
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