I want to check if my understanding of a spanning tree (for undirected and connected graphs) is correct.
From, what I have read online. A spanning tree is a subset of a graph, it contains the same amount of vertices of the graph, however it has a minimum amount of edges. There can also be many different spanning trees for a graph.
I have seen some illustrations of spanning trees and their graph so i have tried to come up with my own example.
So this image shows a house shaped graph. If I was to get rid of one edge in that house graph, this would be a spanning tree since there is an alternate pathway to get from one node to another.
I could also potentially get rid of two edges if I make sure that there is still a path that exists between the two nodes.
Am I correct in this assumption?