# algorithm that finds minimal vertex cover of a given vertex

i am looking for a simple algorithm that gets as an input an undirected graph and a vertex in the graph and outputs the minimal vertex cover that v belongs to.

not sure on how to do it correctly, here's my attempt:

for a given undirected graph $$G=(V,E)$$ and a vertex $$v \in G$$

1)$$edges \leftarrow \emptyset$$

2)remove adjacent edges to given vertex v(given in the input)

3)while there are edges in graph G:

3.1)$$edges \leftarrow {u,v}$$

3.2)$$G\:\leftarrow \:G\:\:\ \:\:\left\{u,v\right\}$$ (doesn't let me mark it correctly, but i meant remove {u,v} from G. doesn't give me to write \ correctly

3.3)return |x|+1 (including v we got from the input)

how to make it better? would appreciate seeing better algorithms for this and explanations/insights so i can learn