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connected(+Graph)

Guarantees that an undirected graph Graph is connected.

Graph: A graph.

Description

Guarantees that an undirected graph Graph is connected, i.e., that each vertex is reachable from any other one.

Fail Conditions

Fails if Graph is not an undirected graph variable or if Graph can not be constrained to be connected.

Examples

?- connected(G).
No.

?- V`::[1,2]..[1,2,3,4], E`::[]..[[1,3],[2,4],[3,1],[4,2]], undirgraph(G,V,E), connected(G).
No.

?- V`::[1,2]..[1,2,3], E`::[]..[[1,2],[1,3],[2,1],[2,3],[3,1],[3,2]], undirgraph(G,V,E), connected(G), graph_labeling(G).
V = [1, 2]
E = [[1, 2], [2, 1]]
G = undirgraph([1, 2], [[1, 2], [2, 1]])
Yes ? ;

V = [1, 2, 3]
E = [[1, 3], [2, 3], [3, 1], [3, 2]]
G = undirgraph([1, 2, 3], [[1, 3], [2, 3], [3, 1], [3, 2]])
Yes ? ;

V = [1, 2, 3]
E = [[1, 2], [2, 1], [2, 3], [3, 2]]
G = undirgraph([1, 2, 3], [[1, 2], [2, 1], [2, 3], [3, 2]])
Yes ? ;

V = [1, 2, 3]
E = [[1, 2], [1, 3], [2, 1], [3, 1]]
G = undirgraph([1, 2, 3], [[1, 2], [1, 3], [2, 1], [3, 1]])
Yes ? ;

V = [1, 2, 3]
E = [[1, 2], [1, 3], [2, 1], [2, 3], [3, 1], [3, 2]]
G = undirgraph([1, 2, 3], [[1, 2], [1, 3], [2, 1], [2, 3], [3, 1], [3, 2]])
Yes