True or False: The highest cost edge in a graph cannot be in an MST. If true, prove it. If false, show an example in which it is included. True or False: The highest cost edge in a cycle within a graph cannot be in an MST. If true, prove it. If false, show an example in which it is included. Give an example of a graph in which the highest weighted edge will not be in the MST, but will be in a shortest path tree from a given node when running Dijkstra’s algorithm. Note: you need to provide the graph with all weights, and select a source node for Dijkstra that will include the highest weighed edge.
The questions below assume weighted undirected graphs with distinct edge weights.
True or False: The highest cost edge in a graph cannot be in an MST. If true, prove it. If false, show an example in which it is included.
True or False: The highest cost edge in a cycle within a graph cannot be in an MST. If true, prove it. If false, show an example in which it is included.
Give an example of a graph in which the highest weighted edge will not be in the MST, but will be in a shortest path tree from a given node when running Dijkstra’s
weighed edge.
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