Question

Simple graph with 35 edges have four vertices of degree 5, five vertices of degree 4 and four
vertices of degree 3 then how many vertices are there with degree 2.
12
18
6
9​

Answer 1

Answer:

With handshaking lemma, I get this:

2e=26⟹e=132e=26⟹e=13

Then with Euler's formula, I get:

6−13+f=2⟹f=96−13+f=2⟹f=9

However, since e≤3v−6e≤3v−6 for a simple, connected, planar graph I would get:

13≤3(6)−613≤3(6)−6

13≤1213≤12

I can't figure out how I could get 9 faces for my graph. I can only get 8 faces as shown here:



This is the best attempt I had on this problem with no success.

Step-by-step explanation:

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