The highway distance between 6 cities named (A . G) are illustrated in the following adjacency matrix: .... B A 0 19 28 18 40 19 10 16 17 D 8. 18 16 14 10 40 8. 14 12 28 17 10 12 lo lo OEF lo D7 lo %3D Alo N

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The highway distance between 6 cities named (A . G) are illustrated in the following
adjacency matrix:
ABC
DE
A07
19
28
18 40
16
16
10
10
17
10
19
18
14
E
40
14
12
28
17
10 12
a) Draw the graph.that represent such adjacency matrix
b) List the right sequence of nodes traversed by the DFS and BFS algorithm
starting from node A.
c) Does this graph possess a Euler circuit/path?, why? If any of them does not
exist, how the graph can be modified to have one?
d) Draw the minimum spanning tree of this graph
e) Use the Dijkstra's algorithm to determine the shortest paths from city (A) to all
other cities, Determine the shortest path and cost from node A to node E
[Hint: implement the algorithm step by step to show which node will be added in
sequence]
f) Determine the shortest paths between all pairs of nodes using Floyd-Warshall
algorithm.
8 o
0o ko
lo loc
Transcribed Image Text:The highway distance between 6 cities named (A . G) are illustrated in the following adjacency matrix: ABC DE A07 19 28 18 40 16 16 10 10 17 10 19 18 14 E 40 14 12 28 17 10 12 a) Draw the graph.that represent such adjacency matrix b) List the right sequence of nodes traversed by the DFS and BFS algorithm starting from node A. c) Does this graph possess a Euler circuit/path?, why? If any of them does not exist, how the graph can be modified to have one? d) Draw the minimum spanning tree of this graph e) Use the Dijkstra's algorithm to determine the shortest paths from city (A) to all other cities, Determine the shortest path and cost from node A to node E [Hint: implement the algorithm step by step to show which node will be added in sequence] f) Determine the shortest paths between all pairs of nodes using Floyd-Warshall algorithm. 8 o 0o ko lo loc
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