How can you draw a graph with 6 vertices and 9 edges without crossing any lines?! Its driving me crazy!!?

Question

I simply cannot figure out how to draw this graph without crossing at least one time. please help!

That was a good answer, and it works nicely. I suppose I left out an important part of the question though (I was too general). You have to have vertices a,b,c,d,e,f and edges ab,ad,af,bc,be,cd,cf,de,ef.

Answer 1

Each edge will connect to two vertices. So nine edges will need 9*2 = 18 connections to vertices. So some vertices will have more than one line segment connecting to it.

Draw a regular hexagon. Now choose one of the vertices. It doesn't matter which one. Draw three more line segments from that vertex to the remaining three vertices it is not already connected to. That's it.

You have:

1 vertex with 5 edges connecting with it
3 vertices with 3 edges connecting with them
2 vertices with 2 edges connecting with them

That's 6 vertices with

1*5 + 3*3 + 2*2 = 5 + 9 + 4 = 18 edges connecting with them

And 18 connecting edges means 18/2 = 9 edges since each edge has to connections.