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Oct 9 |
comment |
Minimum word length for an unusual set of generators of the symmetric group
By the way, I knew about this problem previously but did not recognise it immediately. I computed a few of the values of the diameter in magma and then searched the OEIS for the corresponding sequence together with the word "diameter". The only hit was the right one. This is a good methodology to follow for this type of question. |
Oct 9 |
answered | Minimum word length for an unusual set of generators of the symmetric group |
Oct 8 |
comment |
Minimum word length for an unusual set of generators of the symmetric group
Isn't this just prefix reversal? In other words, you are asking for the diameter of the "pancake graph". This is open but see oeis.org/A058986 for lots of information. |
Oct 3 |
answered | When is Aut(G) the symmetric group of an Aut(G)-invariant generating set? |
Oct 3 |
comment |
When is Aut(G) the symmetric group of an Aut(G)-invariant generating set?
The cyclic group of order 6 is also an example. |
Sep 25 |
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What do we know about isospectral Cayley graphs?
@user6818 I already gave an example. The complete graph is a Cayley graph for any group of the appropriate cardinality (finite or not). Thus, in some extreme cases, it is impossible to recover any information about a group from a Cayley graph except its order. If you want more, then you need to tell us something about what you are assuming about the Cayley graphs. |
Sep 25 |
comment |
What do we know about isospectral Cayley graphs?
@Paul Siegel Claiming that "the Cayley graph of a finite group is completely uninteresting" is inflammatory and, in fact, completely wrong. I'm assuming this is a troll. Moreover, my comment did not even assume finiteness... |
Sep 25 |
comment |
What do we know about isospectral Cayley graphs?
I apologise in advance for this trivial comment: the complete graph is a Cayley graph for every group of the appropriate cardinality. Hence, even knowning that two groups have isomorphic Cayley graphs doesn't tell you much about the groups. You'll probably need to make your question more precise. |
Sep 20 |
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Existence of neighborhood inclusion for 4-chordal graphs
I think you mean "Up to symmetry" rather than "By symmetry". |
Sep 10 |
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What are smallest finite images of triangle groups?
Rather than using the SmallGroup library, you might want to use the lowindexnormalsubgroup command in magma on the triangle groups, you'll probably be able to get much further. |
Sep 4 |
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Are there number-theoretic graphs that are far from being isomorphic
For example, take the star on n vertices and the path on n vertices (both with n-1 edges). In this case, $\epsilon$ will be close to 1 no? It shouldn't be hard to generalise this example for different number of edges... |
Sep 4 |
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Are there number-theoretic graphs that are far from being isomorphic
It seems easier to simply take graphs with extremely different degree sequences. |
Aug 27 |
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Cubic Cayley (undirected) graphs
I'm a bit confused about your last paragraph. Clearly, graphs of type A and B are not ``Cayley isomorphic'', but what is meant by the first sentence? Certainly the same group can give rise to graphs of type A and B, even (graph) isomorphic ones. |
Aug 27 |
answered | Cubic Cayley (undirected) graphs |
May 15 |
awarded | Revival |
May 15 |
answered | simple graphs of degree 16 with a semiregular normal subgroup isomorphic to the quaternion group $Q_8$ |
May 10 |
comment |
Triple Transitive Graphs
I only knew that the groups of rank 3 were classified and assumed that the graphs of rank 3 also were. After failing to find a reference and asking around a bit, it seems that they havn't really been explicitly listed anywhere, although how to do it is clear, at least in principle. It may be that the extra information you have in your situation (for example the girth) would allow one to finish case iv) without findind all the rank 3 graphs. |
May 1 |
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Triple Transitive Graphs
More specifically, aren't graphs in (iv) rank 3 graphs, which have been classified? |
May 1 |
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Triple Transitive Graphs
On the other hand, this paper predates the classification of finite simple groups and this seems like the kind of question where the classification could make a big difference (for example, the Higman-Sims graph involves a sporadic simple group, and, as noted in the sketch of the proof in the paper under question, a vertex-stabiliser acts 3-transitively on its neighbours, and 3-transitive groups were only classified post-classification, which might play a role.) Do you have access to reference [1] from the paper? That might be helpful, to see how the Higman-Sims graph comes up. |
Apr 23 |
awarded | Nice Question |