The document discusses Euler's formula in mathematics. It establishes the relationship between the number of vertices, edges, and regions of any connected graph as V - E + R = 2. It then provides results on the maximum number of edges for planar graphs with a certain number of vertices. Finally, it gives an example problem asking to determine the number of regions, degree of each region, and identify the exterior region for a sample graph.

1. Subject:- Maths
Faculty Name:- Ms. Megha Sharma
Made by:- Rahul Sharma

2. It establishes the relationship between the
number of vertices(v), the number of edges(e)
and number of regions(r) of any connected graph.
Formula : V-e+r=2

3. Results
Let G be a connected planner graph with ‘v’
vertices and ‘e’ edges where number of vertices
v≥3, then e≤3v-6.
A complete graph is planner if n≥4.
If G is a connected simple planner graph with
v≥3 vertices and ‘e’ edges and no circuit of
length 3 then e≤2v-4.
The sum of the degrees of the regions of a map
is equal to twice the number of edges.

4. Example
Ques. Consider the following graph and find
a) How many regions are there ?
b) Find the degree of each region?
c) Which region is exterior?
G 1 G 2