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Dear GAP-forum,

Drew Krause wrote:

Apologies for the earlier post; 'CollapsedAdjacencyMat(g)' will give an

adjacency matrix, as I discovered.

This is not correct in general.

In GRAPE (2.3 and above), if gamma.group is transitive on the

vertices of gamma then `CollapsedAdjacencyMat( gamma )' returns the

collapsed adjacency matrix of gamma, collapsed with respect to

Stabilizer(gamma.group,1), which may or may not be trivial.

However, `CollapsedAdjacenyMat( Group(()), gamma )' will always return

the (uncollapsed, ordinary) adjaceny matrix of the graph gamma in

GRAPE. (See the documentation for CollapsedAdjacencyMat to see what

this function does in general.)

For example (using GRAPE 4.0 under GAP4b5, but GRAPE 2.31 behaves

similarly):

gap> J:=JohnsonGraph(4,2); rec( isGraph := true, order := 6, group := Group([ (1,4,6,3)(2,5), (2,4)(3,5) ]), schreierVector := [ -1, 2, 1, 1, 1, 1 ], adjacencies := [ [ 2, 3, 4, 5 ] ], representatives := [ 1 ], names := [ [ 1, 2 ], [ 1, 3 ], [ 1, 4 ], [ 2, 3 ], [ 2, 4 ], [ 3, 4 ] ], isSimple := true ) gap> CollapsedAdjacencyMat(J); [ [ 0, 4, 0 ], [ 1, 2, 1 ], [ 0, 4, 0 ] ] gap> CollapsedAdjacencyMat(Group(()),J); [ [ 0, 1, 1, 1, 1, 0 ], [ 1, 0, 1, 1, 0, 1 ], [ 1, 1, 0, 0, 1, 1 ], [ 1, 1, 0, 0, 1, 1 ], [ 1, 0, 1, 1, 0, 1 ], [ 0, 1, 1, 1, 1, 0 ] ]

Drew Krause continues:

Another question: has anyone developed a 'grape' algorithm for

discovering a graph's Eulerian path, if it exists?

Not that I know of.

Regards, Leonard Soicher.

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