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asymmetric(+Graph)

Ensures Graph is asymmetric

Graph: A graph.

Description

Ensures that for every edge (x,y) added to the Graph the symmetric edge (y,x) is removed.

Fail Conditions

Fails if Graph is not a graph variable or if Graph can not be enforced to be asymmetric.

Resatisfiable

Examples

?- asymmetric(G).
No.
 
?- V`::[]..[1,2,3], E`::[[2,3],[3,2]]..[[1,2],[1,3],[2,1],[2,3],[3,1],[3,2]], dirgraph(G,V,E), asymmetric(G).
No.
 
?- V`::[]..[1,2,3], E`::[]..[[1,2],[1,3],[2,1],[2,3],[3,1],[3,2]], dirgraph(G,V,E), asymmetric(G).
V = V{cardinal([[]:0, [1, 2, 3]:3], Card{cardinal : _658, fd:[0..3]}, _550, _551, _552, [], [], ['SUSP-_2571-susp'], ['SUSP-_2181-dead'])}
E = E{cardinal([[]:0, [[1, 2], [1, 3], [2, 1], [2, 3], [3, 1], [3, 2]]:6], Card{cardinal : _867, fd:[0..6]}, _759, _760, _761, [], ['SUSP-_3006-susp', 'SUSP-_2581-susp'], [], ['SUSP-_2882-dead'])}
G = dirgraph(V{cardinal([[]:0, [1, 2, 3]:3], Card{cardinal : _658, fd:[0..3]}, _550, _551, _552, [], [], ['SUSP-_2571-susp'], ['SUSP-_2181-dead'])}, E{cardinal([[]:0, [[1, 2], [1, 3], [2, 1], [2, 3], [3, 1], [3, 2]]:6], Card{cardinal : _867, fd:[0..6]}, _759, _760, _761, [], ['SUSP-_3006-susp', 'SUSP-_2581-susp'], [], ['SUSP-_2882-dead'])})
 
?- V`::[]..[1,2,3], E`::[[1,2]]..[[1,2],[1,3],[2,1],[2,3],[3,1],[3,2]], dirgraph(G,V,E), asymmetric(G).
V = V{cardinal([[1, 2] : 2, [3] : 3], Card{cardinal : _688, fd : [2, 3]}, _580, _581, _582, [], [], ['SUSP-_2633-susp'], ['SUSP-_2243-dead'])}
E = E{cardinal([[[1, 2]] : 1, [[1, 3], [2, 3], [3, 1], [3, 2]] : 5], Card{cardinal : _902, fd : [1 .. 5]}, _794, _795, _796, [], ['SUSP-_3117-susp', 'SUSP-_2643-susp'], [], ['SUSP-_2970-dead'])}
G = dirgraph(V{cardinal([[1, 2] : 2, [3] : 3], Card{cardinal : _688, fd : [2, 3]}, _580, _581, _582, [], [], ['SUSP-_2633-susp'], ['SUSP-_2243-dead'])}, E{cardinal([[[1, 2]] : 1, [[1, 3], [2, 3], [3, 1], [3, 2]] : 5], Card{cardinal : _902, fd : [1 .. 5]}, _794, _795, _796, [], ['SUSP-_3117-susp', 'SUSP-_2643-susp'], [], ['SUSP-_2970-dead'])})
 
?- V`::[]..[1,2,3], E`::[[1,2]]..[[1,2],[1,3],[2,1],[2,3],[3,1]], dirgraph(G,V,E), asymmetric(G).
V = V{cardinal([[1, 2] : 2, [3] : 3], Card{cardinal : _658, fd : [2, 3]}, _550, _551, _552, [], [], ['SUSP-_2556-susp'], ['SUSP-_2166-dead'])}
E = E{cardinal([[[1, 2]] : 1, [[1, 3], [2, 3], [3, 1]] : 4], Card{cardinal : _864, fd : [1 .. 4]}, _756, _757, _758, [], ['SUSP-_3040-susp', 'SUSP-_2566-susp'], [], ['SUSP-_2893-dead'])}
G = dirgraph(V{cardinal([[1, 2] : 2, [3] : 3], Card{cardinal : _658, fd : [2, 3]}, _550, _551, _552, [], [], ['SUSP-_2556-susp'], ['SUSP-_2166-dead'])}, E{cardinal([[[1, 2]] : 1, [[1, 3], [2, 3], [3, 1]] : 4], Card{cardinal : _864, fd : [1 .. 4]}, _756, _757, _758, [], ['SUSP-_3040-susp', 'SUSP-_2566-susp'], [], ['SUSP-_2893-dead'])})