5.6: Trees

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Terminology

Definition \(\PageIndex{1}\): Tree

A graph is a tree if and only if it is connected and contains no cycles.

Definition \(\PageIndex{2}\): Leaf

A vertex in a tree is a leaf if and only if it has degree one.

Definition \(\PageIndex{3}\): Spanning Tree.

A graph \(G\) is a spanning tree of a graph \(H\) if and only if \(G\) is a subgraph of HH that contains all the vertices of \(H\) and is a tree.