Question 2: The highway distance between 6 cities named (A .. G) are illustrated in the following adjacency matrix: A BCD E

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Question 2:
The highway distance between 6 cities named (A .. G) are illustrated in the following
adjacency matrix:
ABCD EF
28
A07 19 *
B 7 0
C
10 18 40
19 10 0 16
D 18 16 0 14
14 0
17
10
E
40
12
F
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?
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 ("
„ why?
If any of them
). 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
Transcribed Image Text:Question 2: The highway distance between 6 cities named (A .. G) are illustrated in the following adjacency matrix: ABCD EF 28 A07 19 * B 7 0 C 10 18 40 19 10 0 16 D 18 16 0 14 14 0 17 10 E 40 12 F 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? 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 (" „ why? If any of them ). 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
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