graph

Question

Assume G is connected planar graph that has 14 vertices and 20 regions . All interior regions are bounded by a cycle of length 3(i.e. 3 edges).  The no of edges bounded the interior region is ?

Answer 1

TOTAL NO OF INTERIOR REGION=19

TOTAL NO OF OUTER REGION=1

IN THE CONNECTED PLANAR GRAPH TOTAL NO OF REGION IS GIVEN BY:

R=E-V+2

Total no of edges:

E=20+14-2=32

We know that sum of all the edges in the graph=2e

Also ,Inner region*Degree of each vertex+Outer region*Degree of each vertex=2e

Thus, 19*3+1*x=64,x=7

Exactly 7 edges in outer region. Thus Inner region is bounded by 7 edges.

Comments

first its written sum of edges not vertices written in solution. second 32-7 =25 edges are left not only 7 it seems to me you just copy pasted the answer it is asking for edges and you are answering vertices is there no difference between edges and vertices?

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Before proceeding to further comment do understand handshaking lemma.then you'll understand how it's coming.

https://en.wikipedia.org/wiki/Handshaking_lemma

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and for further clarity also search for bounded keyword of graph then definitely there won't be any doubt.