Timeline for Highly symmetric 6-regular graph with 20 vertices
Current License: CC BY-SA 3.0
12 events
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| Apr 25, 2012 at 20:11 | comment | added | verret | Right. And it would seem that both of the graphs Simon was interested in have chromatic number 4. | |
| Apr 22, 2012 at 14:36 | comment | added | Brendan McKay | If it is one of the last two, it is the second last since there is exactly one triangle on each edge. | |
| Apr 22, 2012 at 14:11 | history | edited | verret | CC BY-SA 3.0 |
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| Apr 22, 2012 at 14:04 | comment | added | verret | I fixed the graph6 notation for the fourth graph, thanks! | |
| Apr 22, 2012 at 14:01 | history | edited | verret | CC BY-SA 3.0 |
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| Apr 22, 2012 at 10:49 | comment | added | Felix Goldberg | verret, are you sure about the fourth graph? My parser stumbles on it? | |
| Apr 22, 2012 at 10:24 | comment | added | Felix Goldberg | Maybe my old g6 parser will be helpful to whoever reads this thread. It's a simple matlab function I wrote back in 2007. If today there are better tools, I'll be glad to retire it. function mat=g6str2matrix(str); % Note: this only works for less than 63 vertices!!! d=double(str); n=d(1)-63; max_e=n*(n-1)/2; mat=zeros(n); Q=dec2bin(d(2:end)-63,6); W=reshape(Q',[],1)'; W=W(1:max_e); W=double(W)-48; ind=find(triu(ones(size(mat)),1)); mat(ind)=W; mat=symmetrize(mat); | |
| Apr 21, 2012 at 20:10 | history | edited | verret | CC BY-SA 3.0 |
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| Apr 21, 2012 at 10:28 | comment | added | verret | As for your question, I am not sure we understand each other. A graph is arc-transitive if its automorphism group is transitive on arcs (ordered pairs of adjacent vertices). Most but not all edge- and vertex-transitive graphs are arc-transitive. I don't know about any relation to Alhambra groups but I am doubtful. | |
| Apr 21, 2012 at 10:26 | comment | added | verret | Maybe the page I should have linked to is the following one : mapleta.maths.uwa.edu.au/~gordon/trans On this page, Gordon Royle has a bunch of files containing all the vertex-transitive graphs on up to 31 vertices in graph 6 format. The files are split in different categories so, if you scroll down, you will find a file containing the 80 connected 6-regular vertex-transitive graphs. It is then simply a matter of checking which are edge-transitive, etc... | |
| Apr 20, 2012 at 22:05 | comment | added | Simon Lentner | Thanks! I'll take a look at the page you linked :-) The graphs do NOT? seem arc-transitive to me, as generall there are arcs on the icosahedron with different "geometric distance"....is that any related to Symmetry patterns in the plane (discrete subgroups of SO(2) or "Alhambra groups")? | |
| Apr 20, 2012 at 12:31 | history | answered | verret | CC BY-SA 3.0 |