S$=$ empty act while G has atleast one edge $,$ find a vertex V of the highest possible degree in G$.$ Add V to S$.$ Remove vertex V from G$,$ along with all edges that hit V$.$ Return S$.$ A vertex cover needs to cover all of the edges where an edge is covered by choosing a vertex from that edge. This algorithm is based on the principle that, by choosing a vertex with the most edges hitting it$,$ we get cover the most edges, What kind of algorithm is this? Is it guranteed to find the smallest vertex error? If so why? If not $,$ give a counter example.