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