Question about graph

The question is Calculate the maximum number of edges in a simple graph with nnodes and k components.

I dont really understand what the question means .. and how to solve this..

Thanks...

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Originally Posted by kakatomy

[FONT=arial]The question is Calculate the maximum number of edges in a simple graph with nnodes and k components.
I dont really understand what the question means .. and how to solve this..

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A component is a maximally connected subgraph of a graph.
You need to check your text material. Some authors allow degenerate components, one vertex, most do not.

Here is an example: Consider a twelve vertex graph with three components having three, four and five vertices.
Then the graph could be $\displaystyle K_3\cup K_4\cup K_5$.
That is a maximum of $\displaystyle 3+6+10=19$ edges in all.

That said, I don't know how to solve the general case.

Quote:

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Originally Posted by Plato

A component is a maximally connected subgraph of a graph.
You need to check your text material. Some authors allow degenerate components, one vertex, most do not.

Here is an example: Consider a twelve vertex graph with three components having three, four and five vertices.
Then the graph could be $\displaystyle K_3\cup K_4\cup K_5$.
That is a maximum of $\displaystyle 3+6+10=19$ edges in all.

That said, I don't know how to solve the general case.

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The question didnt provide anything else so I also dont understand the question....

SOsad :(