Discrete Mathematical Structures by Pearson

Relations and Digraphs 2-17

Solution: The matrix for relation R is

12

34

1

2

3

4

11

11

01

10

01

11

10

11

M

R

=

























and the corresponding diagraph is as follows:

1

2

4

3

Note 2.5 The matrix representing a relation R can also be used to determine whether the relation

is reflexive, symmetric, and transitive. The relation R is reflexive if there is a loop at every vertex

of the directed graph so that pairs (a, a) occur in relation. All elements in the main diagonal of

the adjacency or relation matrix are unity, that is, m

ij

= 1 for all i = j.

Symmetric: The relation is symmetric of m

ij

= m

ji

for all i and j in the relation matrix. That is the

relation matrix ...