1 2 3 and 4 If T has a vertices of degree 2 b vertices of degree 3 and c vertices of degree 4 then how many leaves does it have Question 6 For n 3 how many Hamilton cycles are there in a complete graph on n vertices Keep in mind that we define cycles as sequences of vertices for example a b c a and b c a b are two different cycles Question 7 Take integers n ke N such that 2k n and define a graph Gn k as follows The vertices of Gn k are all the k element subsets of n Two vertices A B are adjacent in Gn k if and only if An B List all integers 1 k 5 such that G10 k is Eulerian Question 8 How many even graphs with vertex set n are there