Spanning Tree

Spanning Tree

An spanning tree is a tree that connects all the vertices of the graph and the lower number of edges. Therefore, the spanning tree is always connected. Also, the spanning tree has never had a cycle. A spanning tree is always defined by a graph and remains a subset of that graph. Thus, a disconnected graph can never have a spanning tree.

Spanning Trees Terminologies:

  1. Connected graph: A connected graph is a graph where we can access any vertex from any vertex. Therefore, on a connected graph, all vertices are connected to each other in at least one way.
  2. Undirected graph: A graph where the edges have no specific direction. In the unadulterated graph, the edges vary.
  3. Directed Graph: In this case, the edges do not match. Therefore, we can move from one end to the other. At each end, there is a corresponding guide.
  4. Simple graph: A simple graph is a graph without cycles and loops.

Description of an spanning tree:

Each graph is not directed and connected to a minimum of one opening tree. Consider a graph with V vertices and E number of edges. After that, we will represent a graph like G (V, E). Its open tree will be represented as G ’(V, E’) where E ’⊆ E and the number of vertices remain the same. Therefore, the tree that produces G’s is a G-branch with its own set of the same vertex but the edges may be different.