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.