# Difference between revisions of "Tree (graph theory)"

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− | A '''tree''' is an undirected graph which is both connected and acyclic. Equivalently, a tree is a graph <math>G=(V,E)</math> such that for any two vertices <math>u, v \in V</math> with <math>u \neq v</math>, there is exactly one path connecting <math>u</math> and <math>v</math> in <math>G</math>. Every tree on <math>|V|=n</math> vertices has exactly <math>n-1</math> edges. | + | A '''tree''' is an undirected [[Graph (graph theory)|graph]] which is both connected and acyclic. Equivalently, a tree is a graph <math>G=(V,E)</math> such that for any two vertices <math>u, v \in V</math> with <math>u \neq v</math>, there is exactly one path connecting <math>u</math> and <math>v</math> in <math>G</math>. Every tree on <math>|V|=n</math> vertices has exactly <math>n-1</math> edges. |

## Latest revision as of 16:51, 2 November 2020

A **tree** is an undirected graph which is both connected and acyclic. Equivalently, a tree is a graph such that for any two vertices with , there is exactly one path connecting and in . Every tree on vertices has exactly edges.