Prove that a minimum spanning tree of a graph component must include a shortest edge. It is possible, in Dijkstra’s algorithm, that an edge removed from the priority queue is not useful: it takes us to a previously visited node. Some of these extraneous edges can be avoided by not placing an edge in the priority queue if the destination has already been visited. Is it still possible to encounter an edge to a previously visited node?

Q: Start with node s and apply the Dijkstra’s algorithm step by step. Show the priority queue at each…

A: Examine the working of Dijkstra's algorithm in the graph

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A: I have solved this in java

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A: The solution for the above given question is given below:

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A:

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A: Note:- As per our bartleby answering guideline, we can answer only first three sub-part of the…