the following graph represents the computers in an office building and the length of wire needing to connect…

Explanation:

Step1: List all edges and their weights

Edges and weights: $(v_2,v_4) = 4$, $(v_4,v_5)=2$, $(v_5,v_7)=2$, $(v_7,v_9)=3$, $(v_3,v_6)=2$, $(v_5,v_3)=5$, $(v_2,v_5)=7$, $(v_1,v_2)=9$, $(v_2,v_3)=8$, $(v_1,v_3)=12$, $(v_4,v_7)=10$, $(v_5,v_6)=11$, $(v_7,v_8)=4$, $(v_8,v_9)=13$, $(v_6,v_8)=4$

Step2: Sort edges by weight in ascending order

$(v_3,v_6)=2$, $(v_4,v_5)=2$, $(v_5,v_7)=2$, $(v_7,v_9)=3$, $(v_2,v_4)=4$, $(v_7,v_8)=4$, $(v_6,v_8)=4$, $(v_5,v_3)=5$, $(v_2,v_5)=7$, $(v_1,v_2)=9$, $(v_2,v_3)=8$, $(v_4,v_7)=10$, $(v_5,v_6)=11$, $(v_1,v_3)=12$, $(v_8,v_9)=13$

Step3: Select edges for minimum - spanning tree without creating cycles

Select $(v_3,v_6)$ (weight 2), $(v_4,v_5)$ (weight 2), $(v_5,v_7)$ (weight 2), $(v_7,v_9)$ (weight 3), $(v_2,v_4)$ (weight 4), $(v_7,v_8)$ (weight 4), $(v_6,v_8)$ (weight 4), $(v_5,v_3)$ (weight 5)

Step4: Calculate total weight of selected edges

$2 + 2+2 + 3+4 + 4+4 + 5=26$

Answer:

26