1. ## k-regular graphs

I have a question which says "for every even integer n > 2 construct a connected 3-regular graph with n vertices".

I know what a 3-regular graph is and how to draw one etc etc...

But am i meant to construct graph for every even integer n > 2??

Can somebody tell me if this question means something else? I may be missing the idea here...cheers people!

2. Originally Posted by pupnat
I have a question which says "for every even integer n > 2 construct a connected 3-regular graph with n vertices".

I know what a 3-regular graph is and how to draw one etc etc...

But am i meant to construct graph for every even integer n > 2??

Can somebody tell me if this question means something else? I may be missing the idea here...cheers people!
they want you to, for any even integer n, construct a 3-regular graph with n verices. here's one way to do it: label the vertices as $1,2, \cdots , 2m=n,$ and choose the edges to be:

$(1,2), (2,3), (3,4), \cdots , (2m-1,2m), (2m,1)$ and $(2,2m), (3,2m-1), (4,2m-2),\cdots , (m+1,1).$