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(Solved): Please solve this graph theory problems Question 1 (a) Define what is meant by the degree sequence ...
Please solve this graph theory problems Question 1 (a) Define what is meant by the degree sequence of a graph and by a sequence of integers being graphical. (b) State the Havel-Hakimi Theorem of graphical sequences. (No proof is required.) (c) Determine if the following sequences are graphical. For each graphical sequence construct a graph having this sequence as a degree sequence: (i)
4,4,2,2,1,1, (ii)
5,5,4,3,2,1. Question 2 (a) Use the adjacency matrix of the graph below to determine the number of walks of length 4 from
v_(1)to
v_(3). (b) Explain how the powers of the adjacency matrix can be used to determine if a graph is connected.
