Answer to Question #37893 in Discrete Mathematics for Sujata Roy

Question #37893
A graph G and its complement G have 8 and 7 edges respectively. What is the
number of vertices in G ?
1
Expert's answer
2017-02-24T06:53:52-0500
Let's consider that number of this full graph vertices is x. Than, the number of edges is the product of x and x-1, and this product has to be divided by 2, because the graph is not oriented. Also, the number of edges is 7+8=15 by the problem statement. Thus, we have an equation:

x(x-1)/2 = 15 -> x(x-1)=30

The roots of this equation are 6 and -5, but in order to x is the number of vertices , x >=0, so x is 6.

Answer. 6 vertices.

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Comments

Assignment Expert
20.12.13, 15:06

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Sujata Roy
20.12.13, 10:25

Thank you.

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