$(5$ points$)$ Let $G=(V,E)$ be a simple, connected graph. If $|V|=n$ and $|E|=m,$ which of the following statements are true? Select all the correct ones.

a$)m=(n^2)$

b$)m=O(n)$ if $G$ is a bipartite graph

c$)m=O(n)$ if all the vertices have the same degree $d,$ a fixed constant.

d$)$ None of the above is correct.

$(10$ points$)$ For the directed graph G below, find an Euler path $($if it exists$)$ and a Hamiltonian path $($i exists$).$ List the vertices of the respective path in order of traversal; write N$/$A if the path does not ex