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Prufer Code/ LabeledTreeToCode Bug?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg104530] Prufer Code/ LabeledTreeToCode Bug?
*From*: Thomas Dowling <thomasgdowling at gmail.com>
*Date*: Tue, 3 Nov 2009 02:54:22 -0500 (EST)
Hello,
1. I am interested in generating the Prufer code for the following simple
graph which I generate as follows:
Needs["Combinatorica`"]
Needs["GraphUtilities`"]
In[137]= gr1 = MakeSimple[
ToCombinatoricaGraph[{2 -> 4, 4 -> 3, 3 -> 1},
Method -> "CircularEmbedding"]];
2. I can visualize the graph as follows, and all is well (it is as I
expect, with no edge between vertices 1 and 2):
In[140]= ShowGraph[gr1, EdgeColor -> Orange, VertexColor -> LightYellow,
VertexLabelPosition -> Center, VertexStyle -> Disk[Large]]
3. However, if I now generate the Prufer code for gr1, I get a strange
result.
In[141]= LabeledTreeToCode@gr1
Out[141]= {2, 3}
4. Firstly, the above Prufer code is clearly wrong: it surely should be
{3,4}?
Secondly, if I use EdgeList, I also get an apparently wrong answer:
In[143]= EdgeList[gr1]
{{1, 2}, {2, 1}, {2, 3}, {3, 2}, {3, 4}, {4, 3}}
Why the edge between vertices 1 and 2?
5. If I 'work backwards' I do not get back the original graph:
In[144]= pcgr1 = CodeToLabeledTree[{2, 3}];
ShowGraph[pcgr1, VertexLabel -> True, EdgeColor -> Orange,
VertexColor -> LightYellow, VertexLabelPosition -> Center,
VertexStyle -> Disk[Large]]
In[145]= EdgeList[pcgr1]
Out[145]= {{1, 2}, {2, 1}, {2, 3}, {3, 2}, {3, 4}, {4, 3}}
The EdgeList is correct for pcgr1, but pcgr1 is not identical with gr1!
6. Finally, if I work with the expected Prufer code, I get a graph and
EdgeList consistent
with what I expected for gr1 but did not get:
In[148]= gr3 = CodeToLabeledTree[{3, 4}];
In[149]= ShowGraph[gr3, EdgeColor -> Orange, VertexLabel -> True,
VertexColor -> LightYellow, VertexLabelPosition -> Center,
VertexStyle -> Disk[Large]]
In[150]= EdgeList[gr3]
Out[150]= {{1, 3}, {2, 4}, {3, 1}, {3, 4}, {4, 2}, {4, 3}}
7. I am working with Mathematica 7.0.0 on a Mac Powerbook G4 (non-Intel)
with OS X v 10.5.8.
Have I missed something or is this a bug?
I am also wondering if others can reproduce
this behaviour on other systems, in particular with Mathematica 7.0.1.
Any help / workaround will be greatly appreciated.
Thanks,
Tom Dowling
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