Question

Find all circuits of length three in the directed graph in Exercise 16.

Short answer

All circuits of length three in the directed graph in Exercise 16 are,

\(\begin{array}{l}a,b,e,a;\;a,d,e,a\\b,c,c,b;\;b,e,a,b\\c,c,b,c;\;c,b,c,c\\d,e,e,d;\;d,e,a,d\\e,a,b,e;\;e,e,d,e;\;e,d,e,e\end{array}\)

Step-by-step solution

Given

The graph is,

Definition of Circuit

A circuit is a path that starts and ends at the same vertex.

A reference point for a circuit is a designated starting point.

Determine the Circuit

All circuits of length three in the directed graph in Exercise 16 are,

\(\begin{array}{l}a,b,e,a;\;a,d,e,a\\b,c,c,b;\;b,e,a,b\\c,c,b,c;\;c,b,c,c\\d,e,e,d;\;d,e,a,d\\e,a,b,e;\;e,e,d,e;\;e,d,e,e\end{array}\)