Graph Theory - connection proof

  • Thread starter oneamp
  • Start date
  • #1
219
0

Homework Statement



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

Homework Equations



??

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
 

Answers and Replies

  • #2
34,904
6,647

Homework Statement



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

Homework Equations



??

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?
 
  • #3
219
0
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
Office_Shredder
Staff Emeritus
Science Advisor
Gold Member
4,435
518
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
219
0
That helped, thank you.
 

Related Threads on Graph Theory - connection proof

  • Last Post
Replies
3
Views
548
  • Last Post
Replies
3
Views
673
  • Last Post
Replies
21
Views
6K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
0
Views
4K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
11
Views
2K
  • Last Post
Replies
5
Views
805
Top