c) Find the shortest paths from source A to all the vertices using Dijkstra algorithm. Fill out the following table: Step Set S 0 {} 1 A (D/P) 01- B (D/P) ∞0 /- C(D/P) ∞0 /- D (D/P) E (D/P) ∞0 /- ∞o /- F (D/P) ∞0 /- G(D/P) ∞o /-

Question 5: Consider the following graph. Find the shortest path from 'a' to all other vertices using Dijkstra's algorithm. Draw graph diagrams to show all intermediate steps. (. 1 4 3 4 a i 3 с 1 2 d 80 g 3

c) Find a Hamiltonian Cycle starting at vertex A. Draw the Hamiltonian Cycle on the graph and list the vertices of the cycle. K L M A B E F G H J Note: A Hamiltonian Cycle is a simple cycle that traverses all vertices. A simple cycle starts at a vertex, visits other vertices once then returns to the starting vertex. For instance, if the vertices of Ks were labeled A, B, C, D, E, one Hamiltonian Cycle would be ABCDEA.

1) The following is a directed graph. 2 11 2 3 5 1 2 9 3 2 3 16 6 6 N 2 T Apply any shortest path algorithm from the source O. Show every step. 8