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The maximum number of possible edges in an undirected simple graph with $100$ vertices and $5$ components is ___

Maximum number of possible edges in an undirected simple graph with 100 (N) vertices and 5 (K) components is

=> $\left ( N - K \right )\left ( N - K + 1 \right ) / 2$

=> 4560
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### 1 comment

maximum no of edges is possible if we assign only one vertex to each component and at the last component we will assign all the vertices
we know component is a tree to each component must have a root/one vertex
4 component has 4 vertices and at 5th component we are left with 96 vertices
so maximum no. of edges = C (96,2)
=4560