Question

(b) The delay time for a packet travelling between four routers (a, b, c, d) is given in the following table: To b From 1 msec 2 msec a b 2 msec 5 msec 2 msec C 5 msec 5 msec 2msec Draw the relation digraph from the information given by the above table (i) (10/100) (ii) Relation R on set {a, b, c, d} is defined as follows: "xRy if the delay time from router x to router y is more than 3 msec". Write relation R in its matrix form (10/100) (iii Based on the delay time table given above, write a matrix representation of relation H, where relation H is defined as follows: "xHy if there exists a path of length one or a path of length two from router x to router y" (10/100)

Answer 1

1. Answer for part (i) is given in the following figure
   Relation Digraph AU link value OYL in unit 5 of 'msec' 2 to
   
2. Answer for part(ii)

The relation on the set
a, b,c, d
is defined as "
xRy
if the delay time from router to router is more than 3 seconds."

• In our directed graph, we assume that if there is no connection from one node to another, the link weight of the corresponding edge is infinity ($\infty$).
• The delay from one node to the same is assumed to be zero.
• Keeping these two assumptions in mind and looking at the table given in the question, we can write down the relation as,

R(a, d), (b,c), (b, d), (c, a), (c, d), (d, a), (d, b)}

A matrix representation of the same is given in the figure below

Rg a b cd o 7 ao O b O I o C O o O O

• Answer for part(iii)

The relation on the set
a, b,c, d
is defined as "
тНу
if there exists a path of length one or two units from router to router ". Directly from the given delay table, taking only those pairs with delay equal to one or two, we can wrtite as,

H (a, b), (a, c), (6, a), (c, b), (d, c)

The matrix representation of the same is given in the figure below.

​​​​​​​

H a b c d O O QI 9 O O O C L dl o