What is a spanning tree?

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What is a spanning tree?

A spanning tree in graph theory is a subgraph of a connected graph that includes all the vertices of the original graph and forms a tree structure. In other words, it is a subset of the original graph that is both connected and acyclic. A spanning tree does not contain any cycles and is the minimum connected subgraph that can be formed from the original graph. It is called a "spanning" tree because it spans or covers all the vertices of the graph. Spanning trees are useful in various applications, such as network design, optimization problems, and finding the minimum cost paths in a graph.