# D1 Trees

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#1
What is the difference between a tree and a spanning tree? Please could I have a simple explanation since I cannot understand those online.

My understanding of a tree is that it is defined to be a connected graph with no cycles.

Whilst a spanning tree is a tree of a connected graph that connects all the nodes in the original graph.

So how can there be a difference between these?
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5 years ago
#2
Minimal spanning is where it takes the least amount of distance or any unit to make a tree. There are algorithms for this.
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5 years ago
#3
A tree that has some of the points, but not all of the points, of the original graph is not a spanning tree.
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5 years ago
#4
A tree graph is a type of graph, in the same way bipartite graph, and complete graph are. And they refer to the graph as is, that is including all its vertices and edges.

A spanning tree, is a subgraph, it may, or may not, include all the edges of the original graph. A graph can have several different spanning trees.
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#5
(Original post by SeanFM)
A tree that has some of the points, but not all of the points, of the original graph is not a spanning tree.
Are you sure because my text book defines a tree to be a CONNECTED graph hence every node of the original graph must be included in ANY tree not just spanning trees
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5 years ago
#6
(Original post by Mathematicus65)
Are you sure because my text book defines a tree to be a CONNECTED graph hence every node of the original graph must be included in ANY tree not just spanning trees
See the post above.

What you've said about connected isn't true (that every node of the original graph must be included).
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#7
(Original post by SeanFM)
See the post above.

What you've said about connected isn't true (that every node of the original graph must be included).
Okay thank you, I think I understand
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