I am wondering if a vertex can lie on an edge in a planar graph- I am not sure if an edge of this vertex is regarded as crossing the edge on which the vertex lies. I have two questions here:
- Is the actual edge from the vertex tangent to the edge on which the vertex lies?
- Even if it only is tangent, does it still fit the definition of a planar graph that edges don't cross- as crossing would mean it would have to go through the edge and out of the edge, rather than just touching it at a single point?
- Is a vertex simply a point and an edge a line segment in the sense in which these terms are defined in plane geometry?