A half circle, also known as a semi-circle, has no vertices.
Understanding Vertices
A vertex (plural: vertices) is a point where two or more lines or edges meet. Specifically, it's typically defined as the point where two straight lines intersect.
Why a Half Circle Has No Vertices
A half circle is formed by a curved arc (half of a circle's circumference) and a straight line (the diameter). While the endpoints of the diameter might seem like vertices, they aren't because they are the intersection of a curved line and a straight line, not two straight lines.
Analogy
Think of a corner of a square or rectangle. That point is a vertex because it's where two straight lines (the sides) meet. A half circle doesn't have a point like that.