Planar And Non-Planar Graph

→ Planar Graph:

A graph is said to be planar if it can be drawn in a plane so that no edge cross.

Example: The graph shown in fig is planar graph.

• Region of a Graph:

Consider a planar graph G=(V,E).A region is defined to be an area of the plane that is bounded by edges and cannot be further subdivided.

• A planar graph divides the plans into one or more regions. One of these regions will be infinite.

• Finite Region:

If the area of the region is finite, then that region is called a finite region.

• Infinite Region:

If the area of the region is infinite, that region is called a infinite region.

Note: A planar graph has only one infinite region.

Example: Consider the graph shown in Fig.
Determine the number of regions, finite regions and an infinite region.

Solution: There are five regions in the above graph, i.e. r₁,r₂,r₃,r₄,r₅.

There are four finite regions in the graph, i.e., r₂,r₃,r₄,r₅.

There is only one finite region, i.e., r₁

Planar graphs have many applications in discrete mathematics and computer science.

Here are a few examples:

A graph is said to be non planar if it cannot be drawn in a plane so that no edge cross.

Example: The graphs shown in fig are non planar graphs.