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Question

Q1 .   Let G be a connected planner graph with 10 vertices.if the number of edges on each face is three then the number of edges in graph G is _____

A 24     B.20    C.32      D.64

 

Q2.  Let  "a(n)" represent the number of bits of length n containing two consecutive 1s what is the recurrence relation of "a(n)"?

A.    a(n-2) + a(n-1) + 2^n-2

B.     a(n-2) + 2a(n-1) + 2^n-2

C.   2a(n-2) + a(n-1) + 2^n-2

D.   2a(n-2) + 2a(n-1) + 2^n-2

 

Q2 i am getting Option A

Comments

1) A.

2) a

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don't know the answer but do explain how you got Q1 (A) 24

here while applying      "R = E-V+2"

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no . of edges in each region is 3 . Let no. of regions = r

Degree of region = no. edges on the boundary of this region = 3

Now,sum of the degrees of the region is exactly twice the no. of edges in graph ,because each edge occurs on the boundary of a region exactly twice (either in two different region , or twice in the same region)

so, 3*r = 2*e

Now, According to Eulers formulae for Planar Graph , r = e - v + 2

3*(e - v + 2) = 2*e

put v=10

we get e = 24