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 a linking function. 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[ g1=AddEdges[ 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? Thanks for your replies. Leigh

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