GATE Overflow Test Series | Mixed Subjects | Test 4 | Question: 25

Question

Consider a network with $6$ routers $R_{1}$ to $R_{6}$ connected with links having weights as shown in the following diagram.

All the routers use the distance vector based routing algorithm to update their routing tables. Each router starts with its routing table initialized to contain an entry for each neighbor with the weight of the respective connecting link. After all the routing tables stabilize, the number of links in the network that will never be used for carrying any data $=$ ________

Answer 1

Following will be distance vectors of all nodes.

Shortest Distances from $R_1$ to $R_2, R_3, R_4, R_5\;\text{and}\;R_6$

$$R_1 (12, 8, 21, 16, 25)$$

Links used$:R_1-R_2, R_1-R_3, R_2-R_4, R_3-R_5, R_5-R_6$

Shortest Distances from $R_2$ to $R_3, R_4, R_5\;\text{and}\; R_6$

$$R_2 (5, 9, 12, 16)$$

Links used$: R_2-R_3, R_2-R_4, R_4-R_5, R_4-R_6$

Shortest Distances from $R_3$ to $R_4, R_5\;\text{and}\; R_6$

$$R_3(11, 8, 17)$$

Links used$:R_3-R_5, R_5-R_4, R_3-R_5, R_5-R_6$

Shortest Distances from $R_4$ to $R_5\;\text{and}\;R_6$

$$R_4 (3, 7)$$

Links used$:R_4-R_5, R_4-R_6$

Shortest Distance from $R_5\; \text{to}\; R_6$

$$R_5(9)$$

Links Used: $R_5-R_6$

If we mark, all the used links one by one, we can see that all the links are used.

So, the correct answer is $0.$