Write a general Integer Linear Programming (ILP) and ILP for the graph for the following weighted graph of 6 vertices (weight = index . i., e., vertex 1 has weight 1 unit, vertex 2 has weight 2 unit, and so on.)

(a) for Minimum vertex cover

• INSTANCE: Graph G = (V, E).
• SOLUTION: A vertex cover for G, i.e., a subset V V such that, for each edge (u, v) E, at least one of u and v belongs to V'.
• MEASURE: Weight (c) of the vertex cover, i.e., |V|.

(b) for minimum Dominating set

• INSTANCE: Graph G = (V, E).
• SOLUTION: A dominating set for G, i.e., a subset V V such that for all u (V-V) there is a v V for which (u, v) E.
• MEASURE: Weight (c) of the dominating set, i.e., |V|.

Graph Graph