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https://gateoverflow.in/83854/gate1990-1-viii

The above is the link of the question. In the solution it was assumed that the graph is complete. But in the question nothing is mentioned. Also a complete graph doesn’t contain self loops. So what I’m thinking is, if we consider the adjacency matrix of the graph, there will be n^2 elements, so n^2 edges are possible in a directed graph. So according to the question, if m is the number of the edges in the graph, then m = n^2 – m should be the condition.

Please let me know about this!

in Graph Theory by (5 points) | 15 views
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Question saying about Complement of Graph.

Number of Edges in Graph + Number of Edges in Complement Graph = Max Edges 

Max Edges in Any Graph is $^nC_2$ which is Total edges in Complete Graph.

Now you can easily solve it.

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