Question

Suppose that a connected planar simple graph has 12 vertices, each of degree4. Into how many regions does a representation of this planar graph split the plane?

Answer 1

12 regions.

Explanation:

A graph is said to be planar if it could be drawn in a plane simply so no place cross.

Example: The graph established is a planar graph.

Region of a Graph: Consider a planar graph G=(V, E).

A location is defined to be an area of the plane that is bounded thru edges and can not be similarly subdivided.

A graph G= (V, E) is said to be planar if it could be drawn withinside the plane simply so no edges of G intersect at a component apart from a vertex.