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Consider the digraph G = ( V , E ) at the left figure composed of six internally fully connected subgraphs G i , i
Consider the digraph at the left figure composed of six internally fully connected
subgraphs dots, with vertices! Each has vertices with indices ranging
from to ; vertices of : The interconnections between subgraphs
are always from the highest indexed vertex of to lowest indexed vertex of
eg the edge from to goes from to The edges are weighted such that all
edges of each dots,both within and interconnecting have a weight of eg each
edge within and any edge going out of has a weight of while each edge within and
any edge going out of has a weight of
Hint for and : You may apply the algorithms from our online discussions to solve the following
problems; but it may be easier to figure out the graph and solve it directly without using the algorithm.
a Find the shortest path to each vertex in from and draw a graph that shows only these paths with the
weights for each edge on that graph.
b Find ie draw one of the minimum spanning trees of the underlying graph of that minimizes the
average distance between all pairs of vertices where is the shortest path between
vertices and in Show each vertex of and the connecting edges & weights in your MST
c Apply depth first search DFS to the graph above starting at Disregard the weights of edges for this part
of question! Perform your search regarding the vertices' ascending numerical order! Show the final output
order of processed vertices along with the time stamps of the algorithm!
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