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Recall that a tree is a connected acyclic graph. Note that this is similar to but slightly different from a rooted tree that you might have come...
Recall that a tree is a connected acyclic graph. Note that this is similar to but slightly different froma rooted tree that you might have come across before in the context of data structures. In our context the tree does not have any designated root vertex, and is just a graph on n vertices and with m edges.If the graph has no simple cycles but has the property that the addition of any single edge (not already in the graph) will create a simple cycle, then the graph is a tree.If the graph has no simple cycles but has the property that the addition of any single edge (not already in the graph) will create a simple cycle, then the graph is a tree.Prove both of these.
