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Spanning tree - Wikipedia

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In the mathematical field of graph theory, a spanning tree T of an undirected graph G is a subgraph that is a tree which includes all of the vertices of G.[1] In general, a graph may have several spanning trees, but a graph that is not connected will not contain a spanning tree (see about spanning forests below). If all of the edges of G are also edges of a spanning tree T of G, then G is a tree and is identical to T (that is, a tree has a unique spanning tree and it is itself). Several pathfinding algorithms, including Dijkstra's algorithm and the A* search algorithm, internally build a spanning tree as an intermediate step in solving the problem. In order to minimize the cost of power networks, wiring connections, piping, automatic speech recognition, etc., people often use algorithms that gradually build a spanning tree (or many such trees) as intermediate steps in the process of finding the minimum spanning tree.[2] The Internet and many other telecommunications networks have trans

Spanning tree - Wikipedia Jump to content From Wikipedia, the free encyclopedia Tree which includes all vertices of a graph For the network protocol, see Spanning Tree Protocol . For other uses, see Spanning tree (disambiguation) . A spanning tree (blue heavy edges) of a grid graph In the mathematical field of graph theory , a spanning tree T of an undirected graph G is a subgraph that is a tree which includes all of the vertices of G . [ 1 ] In general, a graph may have several spanning trees, but a graph that is not connected will not contain a spanning tree (see about spanning forests below

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