# Hi, Can i get answers to these graph theory questions below. Show that if T is a tree containing at least one vertex of degree 2, then complement T…

Hi,

Can i get answers to these** graph theory **questions below.

(1). Show that if T is a tree containing at least one vertex of degree 2, then complement T is not Eulerian.

(2). Let G be a connected r-regular graph of order n such that complement of G is also connected. Prove that at least one of G and complement of G is Eulerian.

(3). Let G be a connected r-regular graph of order n such that complement G is also connected. Prove that at least one of G and complement of G is Hamiltonian

(4). Prove that for each odd integer n ≥ 3, there exists exactly one Eulerian graph of order n containing exactly three vertices of the same degree and at most two vertices of any other degree.