II. Suppose there are a number of modules to schedule for lectures using as few time slots as possible. If two modules have the same lecturer, then they cannot be scheduled in the same time slot. i. Construct a graph where the vertices are modules, numbered as in the table below, and two vertices are adjacent (connected by an edge) if the modules represented cannot be scheduled at the same time. Node Modules Modules with same lecturer -23 4171 4175, 4174 4172 4174, 4177 4173 4175, 4176, 4177 45 4174 4171, 4172 4175 4171, 4173, 4176, 4177 6 4176 4173, 4175, 4177 7 4177 4172, 4173,4175, 4176 ii. Using a few colours as possible colour the graph to show modules that can be scheduled simultaneously