To prove that a connected graph with every vertex being a leaf has exactly one edge, we can proceed with the following proof by contradiction:
Assume that the graph g has more than one edge. This means there exists at least one vertex v with degree greater than 1. Since g is connected, there must be a path between any two vertices in the graph.
Let's consider the case where we have at least two edges incident to vertex v. Since v is a leaf, each of these edges must connect to different vertices, say v1 and v2.
Now, we can construct a path between v1 and v2 by following the edges incident to v. This path will include vertices other than v, which contradicts our assumption that every vertex in g is a leaf.
Therefore, our assumption that g has more than one edge leads to a contradiction. Thus, g can have only one edge.
let g = (v, e) be a connected graph in which every vertex is a leaf. prove that g has exactly one edge
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