Question

If G is a planar graph, then for any vertex G can be drawn s. t. the vertex is on the boundary of the infinite region.

A) True
B) False
C) Depends on the specific properties of G
D) Not enough information to determine

Answer 1

The statement that any vertex of a planar graph can be drawn so that it is on the boundary of the infinite region is true, thanks to the flexibility of planar graph embeddings. Option B.

Step-by-step explanation:

The statement in question is True. If G is a planar graph, it can indeed be drawn such that any given vertex is on the boundary of the infinite region.

In a planar graph, you can redraw or deform the graph without crossing edges until the desired vertex is on one of the exterior faces of the graph, which is typically considered the infinite region in planar graph drawings.

This is possible due to the flexibility of planar graph embeddings on the plane and the fact that every planar graph can have an embedding where a specific vertex is on the outer face. Option B.