## Abstract For any __d__β©Ύ5 and __k__β©Ύ3 we construct a family of Cayley graphs of degree __d__, diameter __k__, and order at least __k__((__d__β3)/3)^__k__^. By comparison with other available results in this area we show that our family gives the largest currently known Cayley graphs for a wide ra
β¦ LIBER β¦
On Non-Cayley Vertex-Transitive Graphs of Order a Product of Three Primes
β Scribed by Mohammad A. Iranmanesh; Cheryl E. Praeger
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 192 KB
- Volume
- 81
- Category
- Article
- ISSN
- 0095-8956
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β¦ Synopsis
This paper completes the determination of all integers of the form pqr (where p, q, and r are distinct primes) for which there exists a vertex-transitive graph on pqr vertices which is not a Cayley graph.
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We consider finite groups which have connected transversals to subgroups whose order is a product of two primes p and q. We investigate those values of p and q for which the group is soluble. We can show that the solubility of the group follows if q = 2 and p β€ 61, q = 3 and p β€ 31, q = 5 and p β€ 11