# Graph Theory - connection proof

oneamp

## Homework Statement

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

??

## 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

Mentor

## Homework Statement

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

??

## 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

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

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.)

Staff Emeritus