#applied course

Question

how many regions are in the above graph and please explain with region formula also.
r=e-v+(c+1)
my attempt is :

r=5-5+2

r=2

but the rule is twice the no of boundary edges which is (5*2) = sum of region degrees which (4+5=9 ) can someone explain where the fault is

Answer 1

 

   

You have done a little mistake while counting degree of regions.

To find the degree of region in a graph, we suppose that every edge has 2 sides, inner and outer.

Example :- edge e2 has 2 sides, inner side and outer side.

 

Now, the degree of any region = #sides by which the region is surrounded.

In this graph, there are two regions R1 and R2

R1 is closed region (closed by edges e1,e2,e3,e4) whereas R2 is outer region (not closed).

R1 is surrounded by inner side of edges e1,e2,e3,e4 so degree of R1=4.

R2 is surrounded by outer side of edges e1,e2,e3,e4,e5 as well as inner side of edge e5 so degree of R2=6.

So, sum of R1+R2= 10.

 

I hope you got it.