Documentation

Mathematically, a tree is a graph with exactly one path between any two vertexes. A spanning tree of a graph is a tree which includes all vertexes of the graph.

Write a function to construct all spanning trees of a given graph.

You can use graph83 as an example graph to construct spanning trees from.

Examples

>>> length $ spanningTrees graph83
173

>>> toG (Paths [[1,2,4,5,6,7,8],[1,3],[5,10],[7,9]]) `elem` spanningTrees graph83
True

Write a function which returns whether a graph is a tree using spanningTrees.

Examples

>>> isTree graph83
False

>>> isTree $ toG $ Paths [[1,2,3],[1,4,5]]
True

Write a function which returns whether a graph is connected using spanningTrees.

Examples

>>> isConnected graph83
True

>>> isConnected $ toG $ Lists ([1,2,3], [])
False

Graph for use as an example for spanningTrees.