# Graph Theory - connection proof

1. Sep 24, 2013

### oneamp

1. The problem statement, all variables and given/known data

Prove that if a graph has > (n-1)(n-2) /2 edges, it is connected.

2. Relevant equations

??

3. The attempt at a solution

I've drawn several examples and made tables, and I can see that the graph is indeed connected if it has more edges than [(n-1)(n-2)]/2. But what I cannot do so far is prove it. How can I start doing this proof?

Thanks

2. Sep 24, 2013

### Staff: Mentor

What does n represent here?
How does your book define "connected" graph?

3. Sep 24, 2013

### oneamp

n is the number of vertices. Connected graph means that there is no vertex that is not connected to any other by some path. Also the graph is undirected and simple (simple meaning no loops, no more than one edge between any two vertexes.)

4. Sep 24, 2013

### Office_Shredder

Staff Emeritus
You might want to do the opposite proof: if a graph is disconnected, it has fewer than or equal to (n-1)(n-2)/2 edges.

In particular it shouldn't be hard to construct the disconnected graph with the most edges.

5. Sep 24, 2013

### oneamp

That helped, thank you.