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On vertex-transitive, non-Cayley graphs of order pqr

✍ Scribed by Ákos Seress

Book ID
104113946
Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
727 KB
Volume
182
Category
Article
ISSN
0012-365X

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✦ Synopsis

In 1983, D. Maru~ifi 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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