Consider a undirected graph G with vertices { A, B, C, D, E}. In graph G, every edge has distinct weight. Edge CD is edge with minimum weight and edge AB is edge with maximum weight. Then, which of the following is false?ans.G has a unique minimum spanning treeIf AB is in a minimum spanning tree, then its removal must disconnect GNo minimum spanning tree contains ABEvery minimum spanning tree of G must contain CD
Question
Consider a undirected graph G with vertices { A, B, C, D, E}. In graph G, every edge has distinct weight. Edge CD is edge with minimum weight and edge AB is edge with maximum weight. Then, which of the following is false?ans.G has a unique minimum spanning treeIf AB is in a minimum spanning tree, then its removal must disconnect GNo minimum spanning tree contains ABEvery minimum spanning tree of G must contain CD
Solution
The statement "If AB is in a minimum spanning tree, then its removal must disconnect G" is false.
Here's why:
A minimum spanning tree (MST) is a subset of the edges of a graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight.
The removal of an edge from a MST does not necessarily disconnect the graph. This is because a MST is a tree, and a tree is a connected graph. Therefore, even if we remove the edge with the maximum weight (AB in this case), the graph can still remain connected through other edges.
So, the statement "If AB is in a minimum spanning tree, then its removal must disconnect G" is not always true and hence, it is false.
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