The Petersen graph on 10 vertices is the smallest example of a vertex-transitive graph that is not a Cayley graph. In 1983, D. MaruSiE asked, "For what values of n does there exist such a graph on n vertices?" We give several new constructions of families of vertex-transitive graphs that are not Cay
Vertex reconstruction in Cayley graphs
✍ Scribed by Elena Konstantinova
- Book ID
- 108114069
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 740 KB
- Volume
- 309
- Category
- Article
- ISSN
- 0012-365X
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## Abstract In 1983, the second author [D. Marušič, Ars Combinatoria 16B (1983), 297–302] asked for which positive integers __n__ there exists a non‐Cayley vertex‐transitive graph on __n__ vertices. (The term __non‐Cayley numbers__ has later been given to such integers.) Motivated by this problem,
## Abstract For any __d__⩾5 and __k__⩾3 we construct a family of Cayley graphs of degree __d__, diameter __k__, and order at least __k__((__d__−3)/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
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. McK