Malla Reddy College of Engineering and Technology (MRCET)
Department of EEE ( 2017-18 )
Electrical Circuits EEE Illustration: An oriented graph is shown in the figure 1(a) below. Lets us select a tree arbitrarily as shown in
the figure 1(b) below. Then, cut-sets are formed as shown in the figure 1(c) below.
Figure 3: (a) An oriented Graph (b) One of it’s Tree (c) The cut-sets of the Tree
The three fundamental cut-sets are given below
1. Cut-Set-1 : Twig-2 and Link-3
2. Cut-Set-2 : Twig-5 and Links-3&4
3. Cut-Set-3 : Twig-1 and Links-4&3
The following points are to be noted:
1. The number of fundamental Cut-sets are same as the number of Twigs represented by bold
lines.
2. Each Cut-set has only one twig.
3. The direction of the- cut-sets is indicated with arrows on them (same as that of the
corresponding twig ).
Now let us find out the values of the elements of the cut-set matrix [[Qkj] applying the rule at
step 4 in the procedure given above:
1. Cut-Set-1 : a. Elements Q11 , Q14 and Q15 are zero since the branches 1,4 and 5 are not linked with cut-
set-1
b. Elements Q12 and Q13 are +1 since the twig 2 and branch 3 are linked with cut-set-1 and
also in the same orientation as that of cut-set-1.
2. Cut-Set-2 : a. Elements Q21 and Q22 are zero since the branches 1 and 2 are not linked with cut-set-2
b. Elements Q23 and Q25 are +1 since the branches 3 and 5 are linked with cut-set-2 and are
also in the same orientation as that of cut-set-2.
c. Elements Q24 is -1 since the branch 4 is linked with cut-set-2 but it’s orientation is
opposite to that of cut-set-2.
Malla Reddy College of Engineering and Technology (MRCET)
Department of EEE ( 2017-18 )
