Which could be a possible time complexity? I have the following algorithmen (picture) which calculates a Vertex Cover and gets an undirected $G(V,E)$ Graph as input.

The following task is to find the possible Time complexity (estimate) while $n = |V|$, $m = |E|$,
$n \le m + 1$ and $deg(v) = |N(v)|$:
a) $O(n log n)$
b) $O(n + m)$
c) $O(2^n*m)$
d) $O(n^k*m)$
e) $|V| \choose k$ * $\sum_{v \in V} deg(v) $

Clearly a,b cannot be an estimate running time for the algorithm.
e) looks correct, but c and d?
$n=|V|$, and $\sum_{v\in V}deg(v) = 2\cdot |E| = 2m$ (each edge is counted exactly twice).
Take a look here for a proof why ${n \choose k} = \Theta(n^k)$ for a fixed $k$. Substitute everything, and get that also $O(n^k*m)$ is a valid estimate (again, only if $k$ is a fixed number!).
c) Is clearly not a tight bound, since it doesn't even depend on $k$ (although, this statement is by no means a proof).