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
Long cycles in vertex-transitive graphs
✍ Scribed by László Babai
- Publisher
- John Wiley and Sons
- Year
- 1979
- Tongue
- English
- Weight
- 192 KB
- Volume
- 3
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
We prove that every connected vertex‐transitive graph on n ≥ 4 vertices has a cycle longer than (3__n__)^1/2^. The correct order of magnitude of the longest cycle seems to be a very hard question.
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A graph is vertex-transitive or symmetric if its automorphism group acts transitively on vertices or ordered adjacent pairs of vertices of the graph, respectively. Let G be a finite group and S a subset of G such that 1 / ∈ S and S = {s -1 | s ∈ S}. The Cayley graph Cay(G, S) on G with respect to S
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