       graphs

• To: mathgroup at smc.vnet.net
• Subject: [mg60946] graphs
• From: leigh pascoe <leigh at cephb.fr>
• Date: Wed, 5 Oct 2005 02:27:47 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Dear Mathgroup,

I am using Combinatorica to study a board game represented by a graph.
The nxn graph can be created using

<<DiscreteMath`Combinatorica`
n=4;
g=GridGraph[n,n];
ShowGraph[g,VertexNumber\[Rule]True]

The vertices of the graph are numbered from the bottom left in rows,
hence to refer to the matrix (row,column) location of a vertex we define

cellindex[i_,j_]:=n*(n-i)+j;

Now to complete the graph we draw edges from cell(i,j) to cell(i-1,j+1),
where these vertices exist. Here is an example for the 4x4 case

ShowGraph[
g,{{cellindex[2,1],cellindex[1,2]},{cellindex[2,2],
cellindex[1,3]},{cellindex[2,3],cellindex[1,4]},{cellindex[3,1],
cellindex[2,2]},{cellindex[3,2],cellindex[2,3]},{cellindex[3,3],
cellindex[2,4]},{cellindex[4,1],cellindex[3,2]},{cellindex[4,2],
cellindex[3,3]},{cellindex[4,3],cellindex[3,4]}}],
VertexNumber\[Rule]True]

This works ok, but I now have several problems: I would like to write
the above statement as an implied loop for a general nxn gridgraph. I
can't seem to get the correct syntax for this. Can anyone help me?

Then I would like to define some functions on the graph, referring to
the vertices by there grid position. However when I add or delete a
vertex, the numbering on the graph changes. I would like to be able
mutate the graph, but still be able to address vertices by the original
labels, as defined by the cellindex[i,j] function (or any other for that
matter. Any suggestions?

A third problem (bug?) is that in the ShowGraph command the vertex label
on the left loses the left most digit(s) when displayed, as shown above.
I just note that here in case someone at Wolfram wants to fix it.

The documentation for this package is also rather (very) limited. I
bought the book on the package, which gives some more details, but many
functions still remain undocumented. Does anyone know a better source?