Is this star-shaped graph planar?

Question

I've been given that the above graph is planar, but I can't for the life of me redraw it such that none of the edges intersect: the last(10th) edge I draw in on my rough paper always produces an intersection. Would someone prove or disprove the planarity of this graph?

Answer 1

This is the wheel graph $W_6$:

(taken from Wikipedia)

Answer 2

It is planar. Try numbering the five outer vertices and then rearranging them so that you still have the same edges, but now none of them cross. (Hint: if you number them 1 to 5 clockwise from the top, then since there is an edge between 1 and 3, it'd probably help to move 3 to the current position of 2.)

Answer 3

A finite graph is planar iff it doesn't contain either $K_{3,3}$ or $K_5$ as a minor. It's easy to eliminate both possibilities for this graph, so it is planar.

Answer 4

Then just move the six in the center.