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( Tree (graph theory)) In graph theory, a tree is a graph in which any two vertices are connected by exactly one path. Alternatively, any connected graph with no cycles is a tree. A forest is a disjoint union of trees. Trees are widely used in computer science data structures such as binary search trees, heaps, tries, Huffman trees for data compression, etc.

A tree is an undirected simple graph G that satisfies any of the following equivalent conditions

If G has finitely many vertices, say n of them, then the above statements are also equivalent to any of the following conditions

An undirected simple graph G is called a forest if it has no simple cycles.

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