The minimum cost formula can be given as

$$C(x,y) = Max(P) - |f(x) – f(y)|$$

In this case Max(P) = 7 and consider vertical top to bottom approach

A:

C(x,y) = (7 - |5 - 6|) + (7 - |3 - 4|) + (7 - |0 - 1|) = 18

B:

C(x,y) = (7 - |5 - 6|) + (7 - |6 - 4|) + (7 - |4 - 2|) + (7- |1 – 7|) = 17

C:

C(x,y) = (7 - |5 - 6|) + (7 - |6 - 4|) + (7 - |4 - 2|) + (7 - |4 – 1|) + (7 - |0 - 1|) = 26

D:

C(x,y) = (7 - |5 - 6|) + (7 - |3 - 4|) + (7 - |4 - 1|) + (7 - |1 - 7|) = 17

E:

C(x,y) = (7 - |6 - 7|) + (7 - |4 - 2|) + (7 - |1 - 7|) = 11

F:

C(x,y) = (7 - |6 - 7|) + (7 - |6 - 4|) + (7 - |3 - 4|) + (7 - |0 - 1|) = 23

G:

C(x,y)= (7 - |6 - 7|)+ (7 - |6 - 4|)+ (7 - |3 - 4|)+ (7 - |4 - 1|)+7-|1-7|)=22

H:

C(x,y) = (7 - |6 - 7|) + (7 - |4 - 2|) + (7 - |4 - 1|) + (7 - |0 - 1|) = 21

From the calculation, the minimum cost for path E. In other words, path E gives the strongest edge.