Kenneth Rosen Edition 6th Exercise 8.2 Question 54 (Page No. 555)

Question

If G is a simple graph with 15 edges and $\bar G$ has 13 edges, how many vertices does G have?

Comments

edit the que and make that second G to $\bar{G}$

https://gateoverflow.in/27513/simple-graph-with-edges-and-edges-how-many-vertices-does-have

Answer 1

We know ,

a) No of vertices in G = No of vertices in G'

b) No of edges in G + No of edges in G'  =  No of edges in K_n (complete graph of n vertices)  =  n(n-1)/2

So considering these 2 properties , we have :

       n(n-1)/2   =   No of edges in G + No of edges in G'

==> n(n-1)/2   =   15 + 13   =  28

==> n  =  8 [Only positive solution to be considered as n is no of vertices]

Hence each of G and G' contain 8 vertices..