Tree graph theory, Tree graph theory - Definitions, Tree graph theory - Example, Tree graph theory - Facts, Tree graph theory - Types of trees, Tree structure, Tree data structure
A tree is an undirected simple graph G that satisfies any of the following equivalent conditions:
G is connected and has no simple cycles.
G has no simple cycles and, if any edge is added to G, then a simple cycle is formed.
G is connected and, if any edge is removed from G, then it is not connected anymore.
G is connected and the 3-vertex complete graph K3 is not a minor of G.
Any two vertices in G ...
Every tree is a bipartite graph. Every tree with only countably many vertices is a planar graph.
Every connected graph G admits a spanning tree, which is a tree that contains every vertex of G and whose edges are edges of G.
Given n labeled vertices, there are nn−2 different ways to connect them to make a tree. This result is called Cayley's formula.
The number of trees with n vertices of degree d1,d2,...,dn is
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