B tech. Discrete mathematics (I. T & Comp. Science Engg.) Syllabus

DIAGRAMMATIC REPRESENTATIONOF PARTIAL ORDER RELATIONS AND POSETS:

In the previous chapter, we have seen the diagraph of a relation. In this section, we use the diagraphs of the partial order relations, to represent the relations in a very suitable way where there no arrowhead and transitivity shown indirectly known as Hasse diagram.

We understand the Hasse diagram, using following example.

Example 1: Let A = {a, b, c, d, e} and the following diagram represents the diagraph of the partial order relation on A.




Fig.1
Now, we shall draw Hasse diagram from the above diagrams using following rules.

1. 
   Drop the reflexive loops
   

Fig. 2

2. 
   Drop transitive lines
   

Fig. 3

3. 
   Drop arrows