Opened 12 years ago
Last modified 9 years ago
#9136 closed enhancement
more named graphs — at Version 39
Reported by: | Minh Van Nguyen | Owned by: | jason, ncohen, rlm |
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Priority: | major | Milestone: | sage-duplicate/invalid/wontfix |
Component: | graph theory | Keywords: | |
Cc: | Lukáš Lánský | Merged in: | |
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
The database of common graphs currently implements lots of named graphs. Below is a list of named graphs to add to that database. See also ticket #2686:
- Bidiakis cube --- #10307
- Brinkmann graph --- #10310
- Butterfly graph --- #10313
- Friendship graph --- #10315
- Dürer graph --- #10316
- Errera graph --- #10321
- Franklin graph --- #10322
- Goldner–Harary graph --- #10329
- Grötzsch graph --- #10330
- Herschel graph --- #10337
- Moser spindle --- #10338
- Balaban 10-cage --- #12942
- Balaban 11-cage --- #12945
- Double-star snark --- #12952
- Ellingham–Horton graph --- #12989
- fullerene graphs
- Harries graph--- #12952
- Harries–Wong graph --- #12980
- Hoffman graph --- #13038
- Holt graph --- #13411
- Horton graph
- Kittell graph
- Markström graph
- McGee graph --- #12982
- Meredith graph
- Sousselier graph
- Poussin graph
- Robertson graph
- Tutte's fragment
- Tutte graph
- Young–Fibonacci lattice
- Wagner graph --- #12982
- Wiener-Araya graph
- Clebsch graph --- #13038
- Hall–Janko graph --- #13058
- Paley graph --- #13088
- Shrikhande graph --- #10781
- Möbius–Kantor graph (done)
- Nauru graph (done)
- Coxeter graph --- #13038
- Tutte–Coxeter graph --- #12982
- Dyck graph --- #10790
- Foster graph --- #12952
- Biggs–Smith graph --- #12971
- Rado graph
- Folkman graph
- Gray graph --- #12952
- Ljubljana graph --- #12981
- Tutte 12-cage --- #12982
- Blanuša snarks
- Szekeres snark
- Tietze's graph
- Watkins snark
Change History (39)
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comment:7 follow-ups: 8 17 Changed 12 years ago by
Many of these graphs can be trivially generated in GAP using its package Grape (a part of the optional gap_packages spkg) and a library of primitive groups (a part of optional databases_gap spkg). E.g. here is how to get Schlaefli graph:
sage: gap.load_package('grape') sage: gap.eval('G:=NullGraph(PrimitiveGroup(27,12),27);') 'rec( isGraph := true, order := 27, group := PSp(4, 3), \n schreierVector := [ -1, 1, 2, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 1, \n 2, 1, 1, 2, 2, 1, 1, 1, 2 ], adjacencies := [ [ ] ], \n representatives := [ 1 ], isSimple := true )' sage: gap.eval('AddEdgeOrbit(G,[1,2]);') '' sage: gap.eval('VertexDegrees(G);') '[ 10 ]' sage: edges=gap('Orbit(G.group,[1,2],OnSets)') sage: len(edges) 135 sage: schlaefli=Graph([[int(x[1])-1,int(x[2])-1] for x in edges]) sage: schlaefli.degree() [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10] sage: schlaefli.diameter() 2
IMHO there is a more fundamental issue here: Sage should handle such graphs in an efficient way --- just keeping all the edges is pretty much a waste, in particular for bigger examples with hundreds of vertices...
comment:8 Changed 12 years ago by
Replying to dimpase:
Many of these graphs can be trivially generated in GAP using its package Grape (a part of the optional gap_packages spkg) and a library of primitive groups (a part of optional databases_gap spkg).
actually, Grape isn't even needed (I mentioned it for illustrative purposes): to construct the Sage graph, all you need is the following:
sage: edges=gap('Orbit(PrimitiveGroup(27,12),[1,2],OnSets)') sage: schlaefli=Graph([[int(x[1])-1,int(x[2])-1] for x in edges])
PS. To get e.g. Hall-Janko graph, use PrimitiveGroup(100,1)
...
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comment:14 Changed 12 years ago by
Fullerens are in fact a family, that can be generated. G.Brinkmann wrote a program called fullgen http://cs.anu.edu.au/~bdm/plantri/ that does just this, generating all non-isomorphic fullerens with given number of hexagonal faces. Unfortunately it has a weird license, so it cannot be just hooked up to Sage, at least not in a standard package.
comment:15 follow-up: 16 Changed 12 years ago by
I have been sighing at plantri for a while.... I *need* to generate random planar graphs :-p
Nathann
comment:16 Changed 12 years ago by
Replying to ncohen:
I have been sighing at plantri for a while.... I *need* to generate random planar graphs
:-p
Sage way: throw random points on the sphere, generate the facets of their convex closuse (using e.g. cdd), then take the skeleton of the polytope (again, using cdd). Slow, but trivial to code :-)
comment:17 follow-up: 18 Changed 12 years ago by
Replying to dimpase:
IMHO there is a more fundamental issue here: Sage should handle such graphs in an efficient way --- just keeping all the edges is pretty much a waste, in particular for bigger examples with hundreds of vertices...
The underlying architecture is already in place; one needs only to implement a GraphBackend? which represents the graph in question. Implementing simple methods such as has_edge, has_vertex, etc. one can then get the rest of the methods automatically. Check out the source!
comment:18 follow-up: 19 Changed 12 years ago by
Replying to rlm:
Replying to dimpase:
IMHO there is a more fundamental issue here: Sage should handle such graphs in an efficient way --- just keeping all the edges is pretty much a waste, in particular for bigger examples with hundreds of vertices...
The underlying architecture is already in place; one needs only to implement a GraphBackend? which represents the graph in question. Implementing simple methods such as has_edge, has_vertex, etc. one can then get the rest of the methods automatically. Check out the source!
I am not sure I understand how to implement things like add_vertex() and add_edge() - as we would start with a permutation group G, the set of vertices is the domain of the group, and edges cannot be added one by one, but only as whole G-orbits. (Alternatively, not all orbits of G are used as the vertex set, and then adding a vertex would mean adding its G-orbit.)
comment:19 Changed 12 years ago by
Replying to dimpase:
I am not sure I understand how to implement things like add_vertex() and add_edge() - as we would start with a permutation group G, the set of vertices is the domain of the group, and edges cannot be added one by one, but only as whole G-orbits. (Alternatively, not all orbits of G are used as the vertex set, and then adding a vertex would mean adding its G-orbit.)
Well, you can always raise an error in the add_vertex function:
RuntimeError?: You can't add vertices to this kind of graph.
Or something similar. Then whenever you called a function which tried to add a vertex you would get that error, but the rest of the graph library would work just fine.
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comment:23 Changed 11 years ago by
Cc: | Lukáš Lánský added |
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comment:24 Changed 11 years ago by
The following at 3-regular Hamiltonian graphs, hence covered by the LCF construction (http://en.wikipedia.org/wiki/LCF_notation):
Balaban 10-cage L = [-9, -25, -19, 29, 13, 35, -13, -29, 19, 25, 9, -29, 29, 17, 33, 21, 9,-13, -31, -9, 25, 17, 9, -31, 27, -9, 17, -19, -29, 27, -17, -9, -29, 33, -25,25, -21, 17, -17, 29, 35, -29, 17, -17, 21, -25, 25, -33, 29, 9, 17, -27, 29, 19, -17, 9, -27, 31, -9, -17, -25, 9, 31, 13, -9, -21, -33, -17, -29, 29] G = graphs.LCFGraph(70, L, 1) Balaban 11-cage L = [44, 26, -47, -15, 35, -39, 11, -27, 38, -37, 43, 14, 28, 51, -29, -16, 41, -11, -26, 15, 22, -51, -35, 36, 52, -14, -33, -26, -46, 52, 26, 16, 43, 33, -15, 17, -53, 23, -42, -35, -28, 30, -22, 45, -44, 16, -38, -16, 50, -55, 20, 28, -17, -43, 47, 34, -26, -41, 11, -36, -23, -16, 41, 17, -51, 26, -33, 47, 17, -11, -20, -30, 21, 29, 36, -43, -52, 10, 39, -28, -17, -52, 51, 26, 37, -17, 10, -10, -45, -34, 17, -26, 27, -21, 46, 53, -10, 29, -50, 35, 15, -47, -29, -41, 26, 33, 55, -17, 42, -26, -36, 16] G = graphs.LCFGraph(112, L, 1) Bidiakis cube G = graphs.LCFGraph(12, [6,4,-4], 4) Biggs-Smith graph L = [16, 24, -38, 17, 34, 48, -19, 41, -35, 47, -20, 34, -36, 21, 14, 48, -16, -36, -43, 28, -17, 21, 29, -43, 46, -24, 28, -38, -14, -50, -45, 21, 8, 27, -21, 20, -37, 39, -34, -44, -8, 38, -21, 25, 15, -34, 18, -28, -41, 36, 8, -29, -21, -48, -28, -20, -47, 14, -8, -15, -27, 38, 24, -48, -18, 25, 38, 31, -25, 24, -46, -14, 28, 11, 21, 35, -39, 43, 36, -38, 14, 50, 43, 36, -11, -36, -24, 45, 8, 19, -25, 38, 20, -24, -14, -21, -8, 44, -31, -38, -28, 37] G = graphs.LCFGraph(102, L, 1) Dyck graph G = graphs.LCFGraph(32, [5,-5,13,-13], 8) Foster graph G = graphs.LCFGraph(90, [17,-9,37,-37,9,-17], 15) Franklin graph G = graphs.LCFGraph(12, [5,-5], 6) Gray graph G = graphs.LCFGraph(54, [-25,7,-7,13,-13,25], 9) Harries graph G = graphs.LCFGraph(70, [-29,-19,-13,13,21,-27,27,33,-13,13,19,-21,-33,29], 5) Harries-Wong graph L = [9, 25, 31, -17, 17, 33, 9, -29, -15, -9, 9, 25, -25, 29, 17, -9, 9, -27, 35, -9, 9, -17, 21, 27, -29, -9, -25, 13, 19, -9, -33, -17, 19, -31, 27, 11, -25, 29, -33, 13, -13, 21, -29, -21, 25, 9, -11, -19, 29, 9, -27, -19, -13, -35, -9, 9, 17, 25, -9, 9, 27, -27, -21, 15, -9, 29, -29, 33, -9, -25] G = graphs.LCFGraph(70, L, 1) Ljubljana graph L = [47, -23, -31, 39, 25, -21, -31, -41, 25, 15, 29, -41, -19, 15, -49, 33, 39, -35, -21, 17, -33, 49, 41, 31, -15, -29, 41, 31, -15, -25, 21, 31, -51, -25, 23, 9, -17, 51, 35, -29, 21, -51, -39, 33, -9, -51, 51, -47, -33, 19, 51, -21, 29, 21, -31, -39] G = graphs.LCFGraph(112, L, 2) McGee graph G = graphs.LCFGraph(24, [12,7,-7], 8) Möbius–Kantor graph G = graphs.LCFGraph(16, [5,-5], 8) Nauru graph G = graphs.LCFGraph(24, [5,-9,7,-7,9,-5], 4) Tutte 12-cage G = graphs.LCFGraph(126, [17, 27, -13, -59, -35, 35, -11, 13, -53, 53, -27, 21, 57, 11, -21, -57, 59, -17], 7) Tutte–Coxeter graph G = graphs.LCFGraph(30, [-13,-9,7,-7,9,13], 5) Wagner graph G = graphs.LCFGraph(8, [4], 8)
Some of the Fullerene graphs can be expressed in LCF notation as well.
comment:25 Changed 11 years ago by
It's nice to have them explicitly constructed so you get a nice picture in a plot, though. I have a really old patch lying around for the Balaban 11-cage, I'll see if I can rebase it...
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comment:32 Changed 11 years ago by
Well David, all of your graphs are now Sage patches or are included already. My only regret is that I found not nice embedding for Tutte's 12 cage :-/
Nathann
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My god O_O SO you are basically saying I'm not sending enough ? :-D
To be honest I have tried to implement some of them, but felt I should ask for the help of Sage's algebraists... This one, for example : is there any way to build it using Sage's tools ?
http://www.win.tue.nl/~aeb/graphs/Schlaefli.html
Nathann