Directed graph(diagraph)Hasse Diagram Discrete mathematics

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  directed graph

A graph of the given relation.

Let A and B are the two finite sets and R is the relation from A to B.

For a graphical representation of a relation on a set is represented by a point. Each element in a set is represented by a point in diagraph. Those points are called as nodes.

An edge is drawn from one point to another related point. This edges are called as arc.

The direction in the diagraph is represented by an arrow. And all arrows in directed graph with atrows called as directed arcs.

For example:

Draw a  directed graph that represents the relation:

R={(1,1),(2,2),(1,2),(2,3),(3,2),(3,1),(3,3)}




The loops present in the diagraph represents the reflexive property that are (1,1),(2,2),(3,3) the edge from 1 to 2 represents (1,2) and similarly other edges are shown.

Hasse diagram

 Hasse diagram is a diagram which represents partial ordered set in the form of graph without showing its transitive relation.

Steps to draw a Hasse diagram:

  1. Start with a directed graph 
  2. Remove all loops in directed graph (diagraph)
  3. Remove all edges which show transitive relation 
  4. Remove all arrows in directed graph 

Example 1:A={1,2,3,9,18} and consider A divides relation on A. Draw its Hasse diagram.

For a,b belongs to set A the relation R={(1,1),(1,2),(1,3),(1,9),(1,18),(2,2),(2,18),(3,3),(3,9),(3,18),(9,9),(9,18),(18,18)}

Hasse diagram for the given relation:

step1:

Step 2:

step 3:

step 4:





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