Name
Abstract | ||
|---|---|---|
A positive integer n is a Cayley number if every vertex-transitive graph of order n is a Cayley graph. In 1983, Dragan Marui posed the problem of determining the Cayley numbers. In this paper we give an infinite set S of primes such that every finite product of distinct elements from S is a Cayley number. This answers a 1996 outstanding question of Brendan McKay and Cheryl Praeger, which they believe to be the key unresolved question on Cayley numbers. We also show that, for every finite product n of distinct elements from S, every transitive group of degree n contains a semiregular element. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.jctb.2016.06.005 | J. Comb. Theory, Ser. B |
Keywords | Field | DocType |
Vertex-transitive,Cayley graph,Cayley number,Semiregular | Integer,Discrete mathematics,Combinatorics,Vertex-transitive graph,Cayley table,Cayley transform,Cayley's theorem,Cayley graph,Word metric,Prime factor,Mathematics | Journal |
Volume | Issue | ISSN |
122 | C | 0095-8956 |
Citations | PageRank | References |
1 | 0.37 | 7 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ted Dobson | 1 | 1 | 1.38 |
| Pablo Spiga | 2 | 71 | 18.37 |