Hi, I work with GAP and have not much experience with SAGE. I wonder whether there is an easy way to obtain a program with SAGE that gives as output a list of all directed simply laced acyclic connected graphs on n points up to equivalence that is readable for GAP (via the GAP-package QPA).

Here a more detailed description of what the program should do:

Input: A natural number n >=2. Output: The list of directed simply laced acyclic connected graphs on n points up to equivalence. Here we call two such graphs equivalent in case they have the same underlying undirected graph (in case it is a problem to do it up to equivalence, we can first look at the problem without up to equivalence).

Here how to output should look in the first 3 cases for n<=4 so that it is readable for GAP: Note that graphs are also often called quivers. GAP reads those graphs as Quiver(n,[[p1,p2,"a1"],...[pnminusone,pn,"ar"]]) where we name the points pi and the arrows between them as ar for some index sets i and r. (I hope it will be clear with the following examples).

n=2: [Quiver(2,[[1,2,"a1"]])];

n=3: [Quiver(3,[[1,2,"a1"],[2,3,"a2"]])]; (note here that the quiver Quiver(3,[[1,2,"a1"],[2,3,"a2"]]) is equivalent to the quiver Quiver(3,[[1,2,"a1"],[3,2,"a2"]]) since they are equal when looking at their undirected graphs)

n=4: [Quiver(4,[[1,2,"a1"],[2,3,"a2"],[3,4,"a4"]]),Quiver(4,[[1,2,"a1"],[2,3,"a2"],[4,2,"a3"]]); (here we have two non-equivalent quivers).

Thanks you very much for any help.

n=3