1) Explain the data and record structures for the vertex ordering and vertex or edge colouring (or labelling) and a suitably the greedy graph search algorithm in order to solve each of the following problems in time bound indicated. Explain each algorithm along with the vertex or edge colouring (or labelling) on a graph or tree developed in order to teach your algorithm. The graph (or tree) must have at least 18 vertices and a maximum degree of at least 4. The graph must be connected with the minimum degree 3.
2) Determine a smallest-last vertex ordering and plot degree when deleted diagram for following random geometric graphs:
a) G (20, 0.25),
b) G (400, 0.15),
c) G (4,000, 0.06).