Consider the following weighted graph.

$($a$)$ Apply Dijkstra's Algorithm to the graph with $A$ as the source$/$root and draw the graph for EACH

step of the algorithm $($include the initial state!$).$

$($b$)$ Draw the minimum distance spanning tree associated with the algorithm with $A$ as the root.

Label the vertices!

$($c$)$ Suppose a new graph is formed by deleting the edge between $D$ and $E.$ Run Dijkstra's Algorithm

on this new graph with $A$ as the source$/$root$.$ You only need to provide the final graph and

labeling produced by the algorithm.

$($d$)$ Explain how you know the graph from the previous question is disconnected using only the output

of Dijkstra's Algorithm.