5. Prove that any given edge of a connected graph G is a branch of some spanning tree of G.
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Theorem 4.12 Every connected graph has at least one spanning tree. Proof Let G be a connected graph. ... If G has cycles, then on deleting one edge from each of the cycles, the graph remains connected and cycle free containing all the vertices of G. Definition: An edge in a spanning tree T is called a branch of T.
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A connected graph G can have more than one spanning tree
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