Graph - no of regions

Question

Consider 11-regular connected graph of order 8. How many regions are there in planar embedding?

Comments

@Rishabh Gupta 2 it is given in the question that degree of each vertex is 11, it is not given in the question directly that degree of each vertex is 11, but the above graph is "11-regular graph" which means the degree of each vertex is 11.

And then the remaining calculation is given in the above comment.

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@Shubhanshu Yes I understood that part.

But my doubt is if we have say n vertices, then what is the max degree possible for any vertex?? Answer this in general (do not relate it to this question)

I think max degree a vertex can have is n-1. Since a vertex can atmost connect to all other vertices.

So, now coming to the question. How can a graph with only 8 vertices, there can be any vertex with degree 11 ?

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Yes, @Rishabh Gupta 2 I got your point. It means this question is meaningless.

Thanks.

Answer 1

E= n*k/2

  =8*11/2 =44

V=8

R=E-V+2

   =44-8+2

   =38