you are given the following graph describing a vertex$-$cover problem instance.

$1.$represent it as an integer lenear programming problem instance

$2.$ find an optimal solution for it

$3.$ Suppose that you developed a new strategy to solve the vertex$-$cover problem such that "You pick up the vertices in the order of having smallest number of current neighbors while removing every edge incident connected to the currently picked vertex until all the edges are removed. Break the tie cases in favor of the node that comes first in the alphabetical order."

a$.$ Solve the above problem by using the new strategy.

b$.$ is this new strategy optimal?

please explain the third question throughly.