Given the following system below Find the minimal pathsets F

Given the following system below: Find the minimal path-sets Find the minimal cut-sets

Solution

a. The minimal path sets are {1,4,7}, {1,5,8}, {1,5,6,7},{2},{2,3,4,7}, {2,3,5,8}, {2,3,5,6,7}.

b. A cut set must contain at least one point of each path set, otherwise it would not cut. The cut sets are

{1,2}, {4,1,2}, {4,5,2}, {7,1,2}, {7,5,2}, {7,8,2}, {8,1,2}, {8,5,2}, {8,6,2}, {8,7,2}, {5,1,2}, {5,4,2}, {5,7,2}, {6,1,2}, {6,4,1,2}, {6,7,1,2}, {7,1,2}, {7,5,2}, {7,8,2}.

Of these minimal is only {1,2},