Dear All,
I'm having a bit of trouble (at least in my mind) with GRAPE.
I'm interested in subgraphs of the following graph and its associated symmetry
group which I define through the adjacency matrix as follows:
gap>A:=[ [ 0, 1, 1, 1, 1, 0 ],
[ 1, 0, 1, 0, 1, 1 ],
[ 1, 1, 0, 1, 0, 1 ],
[ 1, 0, 1, 0, 1, 1 ],
[ 1, 1, 0, 1, 0, 1,],
[ 0, 1, 1, 1, 1, 0 ] ];;
gap>G:=Group((2,3,4,5),(1,2,6,4));:
gap>LoadPackage("grape");;
gap>gamma:=Graph(G, [1..6], OnPoints, function(x,y) return A[x][y]=1; end, true
);;
gap> UndirectedEdges(gamma);
[ [ 1, 2 ], [ 1, 3 ], [ 1, 4 ], [ 1, 5 ], [ 2, 3 ], [ 2, 5 ], [ 2, 6 ], [ 3, 4
],
[ 3, 6 ], [ 4, 5 ], [ 4, 6 ], [ 5, 6 ] ]
So far so good. Then I define the induced subgraph determined by the vertices
1,2,6
gap>gamma_1_2_6:=InducedSubgraph(gamma,[1,2,6]);;
This should, in my mind anyway, give me the subgraph with the edges [1,2] and
[2,6]. However, when I check this with the UndirectedEdges command I get:
gap> UndirectedEdges(InducedSubgraph(gamma,[1,2,6]));
[ [ 1, 2 ], [ 2, 3 ] ]
This bothers me because 3 isn't a specified vertex, furthermore the
UndirectedEdges command appears to be order dependent?
gap> UndirectedEdges(InducedSubgraph(gamma,[1,6,2]));
[ [ 1, 3 ], [ 2, 3 ] ]
My expectation is that either version of the command should return
[[1,2],[2,6]] and I am very much confused as to why this isn't case.
Any insights are appreciated and thanks in advance,
Bill Butske
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