Which matrix represents the number of walks of length 2 and how many walks of length 2 are in the graph G? b A G

Q3B. Consider the following graph: b a C b and d a and b c and f e and f a and e d and f b and c f e Select all pairs of vertices which are adjacent in the graph.

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?

find the length of a shortest path and a shortestpath between each pair of vertices in the weighted graph. question 3 and 5