question 2 (20 points)\nlisten\nthe following graph represents the computers in an office building and the…

question 2 (20 points)\nlisten\nthe following graph represents the computers in an office building and the length of wire needing to connect them in yards. use kruskals algorithm to connect all the computers.\ndetermine the total amount of wire needed to connect the computers.

Answer

Explanation:

Step1: List all edges and their weights

We have the following edges and weights: ((v_1,v_2,9),(v_1,v_3,12),(v_2,v_3,8),(v_2,v_4,4),(v_2,v_5,7),(v_3,v_5,5),(v_3,v_6,2),(v_4,v_5,2),(v_4,v_7,10),(v_5,v_6,11),(v_5,v_7,2),(v_5,v_8,4),(v_7,v_8,4),(v_7,v_9,3),(v_8,v_9,13))

Step2: Sort edges by weight in ascending order

((v_3,v_6,2),(v_4,v_5,2),(v_5,v_7,2),(v_2,v_4,4),(v_5,v_8,4),(v_7,v_8,4),(v_7,v_9,3),(v_2,v_5,7),(v_3,v_5,5),(v_1,v_2,9),(v_1,v_3,12),(v_4,v_7,10),(v_5,v_6,11),(v_8,v_9,13))

Step3: Select edges for the minimum - spanning tree

Start adding edges one by one as long as they don't create a cycle.

First, add ((v_3,v_6)) with weight 2.
Then add ((v_4,v_5)) with weight 2.
Then add ((v_5,v_7)) with weight 2.
Then add ((v_7,v_9)) with weight 3.
Then add ((v_2,v_4)) with weight 4.
Then add ((v_5,v_8)) with weight 4.

Step4: Calculate the total weight

The total weight of the selected edges is (2 + 2+2 + 3+4 + 4=17)