Skip to main content

All Questions

Filter by
Sorted by
Tagged with
4 votes
2 answers
486 views

Transposition Cayley graphs are planar

Consider the Cayley graph $G$ with vertex set the elements of the symmetric group $S_n$ and generating set the set of minimal transposition generators of the group $S_n$, that is the set $S=\{(12),(13)...
vidyarthi's user avatar
  • 2,089
3 votes
0 answers
57 views

Groups that can occur as graph automorphisms of a fixed size graph

From theorem $4$ and corollary $1$ in this book we have that graph isomorphism has to do with automorphism group of a graph. We also know every group is the automorphism group of a graph by Frucht's ...
Turbo's user avatar
  • 13.9k
3 votes
0 answers
164 views

Generating sets of the symmetric group that yield isomorphic Cayley graphs

Let $S$ and $S'$ be subsets of size $k$ of $\mathfrak{S}_n$. Are there any necessary or sufficient conditions to determine whether or not $S$ and $S'$ yield isomorphic Cayley graphs? Assuming we ...
Anthony Labarre's user avatar