I have tried to show different types of relation in Discreate mathematics.

1. WELCOME

2.  Team Members :
 Name : Razuanull Haque Rain.
ID : 161-15-7198
Name : Tanzina Bithi.
ID : 162-15-739

3. Different Types Of Relations :
1. Reflexive Relation .
2. Symmetric Relation.
3. Anti-symmetric Relation.
4. Transitive Relation.

4. Reflexive Relation :
 In mathematics, a relation R over a set X is reflexive if every element of X is related to itself .
That means :
 Let A be the set {1, 2, 3} and R be the relation
R = {(1, 1),(1, 2),(1,3),(2, 1),(2, 2),(2,3),(3,1 ),(3,2),(3,3)}

5. Symmetric Relation :
 A relation R on a set A is called symmetric if (a, b) ∈ R implies that (b, a) ∈ R for all a, b ∈ A.
That means :
if there is an edge between two elements of the set, then there must
be an edge in both directions.

6. Anti- Symmetric Relation:
 To be antisymmetric, there should not be edges in both directions between two vertices.

7. Transitive Relation :
 A set X is transitive if whenever an element a is related to an element b, and b is in turn
related to an element c, then a is also related to c.
That means :
( 1 , 2 ) , (2 , 3 ) → ( 1 , 3 )
To be transitive, “triangular paths” must be closed.

8. Isomorphism
 Two graphs which contain the same number of graph vertices connected in the same way are
said to be isomorphic.
 In other words, when two simple graphs are isomorphic, there is a bijection (one-to-one
correspondence) between vertices of the two graphs that preserves the adjacency relationship.

9. Conditions to be isomorphic :
Two simple isomorphic graphs must :
 have the same number of vertices,
 have the same number of edges,
 have the same degrees of vertices.
 If one is bipartite the other must be,
 If one has wheel, the other must be……etc.
Note 1: These conditions are necessary but not sufficient to show that two graphs are isomorphic.

10. Are the two graphs isomorphic?

17. Thank You All