Consider a weighted graph in which all the weights on the edges are distinct. Suppose that e is the edge with the largest weight. What is the property that the graph must have in order for e to be in the minimum spanning tree?   Question options:   1)  The graph must be a tree.   2)  The edge e must be incident to a vertex of degree 1.   3)  The weight of e must be close to the next largest weight.   4)  The graph is no longer connected if e is removed.

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Minimum Spanning Tree

A spanning tree is a sub-graph of a connected, undirected graph. It has all the vertices of a graph with the minimum possible number of edges. If a vertex is skipped, then it will not be a spanning tree. The edges of a spanning tree may or may not have weights.