Question

Show that if the directed graph G is self-converse and H is a directed graph isomorphic to G, then H is also self-converse.

Short answer

We have to prove that \(H\) is a self-converse by using the transitivity property.

Step-by-step solution

Identification of given data

The given data is:

• The directed and self-converse graph given is\(G.\)

Concept/Significance of graph isomorphism

A graph Isomorphism is a phenomenon of the same graph appearing in several versions. Isomorphic graphs are examples of such graphs.

Determination of the true statement 

The isomorphic relation has a feature of transitivity.

Consider the directed graph\(G\)and\(G\)is isomorphic to\({G_C}.\)

\(G\)is isomorphic to\({G_C}\),\(G\)is self-converse.However, because\(H\)is isomorphic to\(G,\)using the transitive property\({H_C}\)is also isomorphic to\({G_C}.\)

By combining the foregoing information, can prove that\(H\)is isomorphic to\({H_C}.\)

Thus, the graph\(H\)is also self-converse.