Vertex 1 is a king chicken because \(1\rightarrow 2\), \(1\rightarrow 4\), \(1\rightarrow 5\), \(1\rightarrow 2\), \(1\rightarrow 2\rightarrow 3\).

Vertex 2 is a king chicken because \(2\rightarrow 3\), \(2\rightarrow 4\), \(2\rightarrow 5\), \(2\rightarrow 3\rightarrow 1\).

Vertex 3 is a king chicken because \(3\rightarrow 1\), \(3\rightarrow 4\), \(3\rightarrow 5\), \(3\rightarrow 1\rightarrow 2\).

Vertex 4 is not a king chicken (4 did not beat any vertices).

Vertex 5 is not a king chicken (5 only beat vertex 4 and since vertex 4 didn’t beat any vertices, 5 cannot be a king through vertex 4 either).

Exam Question:

In the following graph, how many king chickens are there? Provide evidence that they are king chickens.