Select the graph that is a spanning tree for the given graph. EC D E B G B G A E A E D E C F C F B G A Q B G B G A A

The given graph is strongly connected. b C True or False True False

Draw a graph that models the connecting relationships in the floorplan below. The vertices represent the rooms and the edges represent doorways connecting the rooms. Vertex F represents the outdoors. F C L₁ A B E Is it possible to find a path through the house that uses each doorway once? If so, enter the sequence of rooms (vertices) visited, for example ABDEA. If it is not possible, enter DNE.

The five departments in the Science Faculty played a round-robin table tennis tournament, in which every department played against every other department once. In each game there was a winner and a loser. A table of one-step and two-step dominances was prepared to summarise the results. Team Botany (B) Chemistry (C) Geology (G) Physics (P) Zoology (Z) one-step dominances two-step dominances 3 2 (a) Use the one-step and two-step dominance values to construct a one-step dominance matrix, clearly explaining the allocation of values for each team. Label the rows as Winners and the columns as Losers. (b) Use the one-step and two-step dominance values to construct a two-step dominance matrix, clearly explaining the allocation of values for each team. Label the rows as Winners and the columns as Losers. Construct the final dominance matrix for this competition by adding together the one-step and two-step dominance matrices. (c) (d) What is the finishing order in this competition?