## Graph Theory Help

Hello Guys ,

I am facing these questions am trying to solve but i need your help to begin.

QUESTION 1)

I have to show that there are more than 6600 non-isomorphic graphs with 8 labeld vertices.

:: I need ideas how to solve it

QUESTION2)
How many vertices (|V|) has a connected regular graf with 22 edges?

NOTE:
In the Discrete And Combinatorials Mathematics book from Ralph Grimaldi i tried to solve a similar question which says to find the number of vertices if let say G is a regular graf with 15 edges.

I did it like this:

2|E| = 30 = k|v|
==> 30/k

which is wrong when i checked the answers at the back of the book. The answer in the book is in the quote:

""
|V| = 1 or 2 or 3 or 5 or 6 or 10 or 30
[In the first four cases, G must be a multigraph; when |V|=30, G is disconnected]

""

if someone can explain to me why the answer is so then i can use it to solve the above question myself

QUESTION 3)
G is a regular bipartite graf. I have to show that G a perfect assignment/allocation has.

::Need help how to begin solving it.