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## If a adjacent has not been.

If n=1 or n=2, the degrees of the vertices is 0 or 1, so there are no cut vertices. For trees with n>2 at least one vertex will have tree with n vertices has n-1 minimum cuts greater than 1.

While exactly how many depends on the graph in question, we can set a min and max: Minimum # of cut vertices: A star shaped tree (one vertex with degree n-1, all other vertices degree 1) would have only one cut vertex (the large degree one). Mar 19, the number of edges will be (n-1) + number of edges required to add (n+1)th node. Every vertex that is added to the tree contributes one edge to the tree. Thus, the number of edges required to add (n+1)th node = 1. Thus the total number of edges will be (n - 1) + 1 = n -1+1 = n = (n +1) - 1.

Thus, P (n+1. Nov 10, This increases the probability that the goal node will be reachable from the first nodes with N-1 cuts in the queue when the times come to evaluate them. However, it is only useful to reduce the search space of nodes with N-1 cuts and not the complexity of the whole search. We already discussed how trees have N-1 distinct minimum cuts.

We know the answer at most something like 2N, because a graph only has roughly 2N cuts. In fact, the answer is both very nice and wedged in between. So the answer is exactly N choose 2, where N is the number of vertices. This is also known as N (N-1)/2. Nov 13, Theorem 7: Every tree with at-least two vertices has at-least two pendant vertices.

Proof: Let the number of vertices in a given tree T is n and n>=2. Therefore the number of edges in a tree T=n-1 using above theorems.

summation of (deg(Vi)) = 2e = 2(n-1) =2n-2Estimated Reading Time: 6 mins.