A railway company is considering opening up some new lines between seven towns A-G. The possible lines and the cost of setting them up, in millions of dollars, are defined in the following graph. 20 B 20 20 30 10 35 E G 40 F a. Use Dijkstra's algorithm to find the minimum cost of connecting the cities starting at city A. Use this format to show all iterations: vertex known dv Pv A B C D E F G b. From (a) list the minimum cost and the path for the following lines: a. A-C b. A-E c. A-F c. Use Kruskal's algorithm to find the minimum cost of opening lines so that it is possible to travel between any two of the towns by rail, state the order the lines should be opened to achieve this minimum cost, draw the final MST. d. Use Prims' algorithm to find the minimum cost of opening lines so that it is possible to travel between any two of the towns by rail, state the order the lines should be opened to achieve this minimum cost, draw the final MST.

A railway company is considering opening up some new lines between seven towns A-G. The possible lines and the cost of setting them up, in millions of dollars, are defined in the following graph. 20 B 20 20 30 10 35 E G 40 F a. Use Dijkstra's algorithm to find the minimum cost of connecting the cities starting at city A. Use this format to show all iterations: vertex known dv Pv A B C D E F G b. From (a) list the minimum cost and the path for the following lines: a. A-C b. A-E c. A-F c. Use Kruskal's algorithm to find the minimum cost of opening lines so that it is possible to travel between any two of the towns by rail, state the order the lines should be opened to achieve this minimum cost, draw the final MST. d. Use Prims' algorithm to find the minimum cost of opening lines so that it is possible to travel between any two of the towns by rail, state the order the lines should be opened to achieve this minimum cost, draw the final MST.