Question

Determine whether the following graphs are self-converse.

a)

b)

Short answer

1. Yes, the graph is self-converse due to the line of symmetry from the vertex d.
2. No, the graph is not self-converse due to its anti-symmetry.

Step-by-step solution

Concept/Significance of directed graph

A directed graph is a graph made up of linked vertices or nodes with all connections pointing from one vertex to the next.

(a) Determination of whether the graph (a) is self-converse

If this graph is self-converse, the relevant isomorphism interchanges c and e, and interchanges a andb, as shown in the diagram below.

The above diagram shows a line of symmetry down from vertex das the original graph back by taking the supplied graph and reversing all of the arrows, and then applying this correspondence. As a result, the graph is self-contradictory.

Thus, the graph is self-converse due to the line of symmetry from the vertex d.

(b) Determination of whether the graph (b) is self-converse

The isomorphism must send b and c back upon themselves in one order or the other if this graph is to be self-converse. However, b's incident edges point in the same direction, but c's does not.

The above diagram shows anti symmetry and there is no isomorphism in the graph. So, its inverse is not self-converse.

Thus, the graph is not self-converse due to its anti-symmetry.