Question: only question 3 2. Consider the network below: (a) Write down the adjacency matrix for the given netw0rk using the formula. 1, if nodes 2'

only question 3

nodes 2' and j are connected by an edge A = [as]:

at\": = . 01 otherWISe. Index your rows and columns in the

2. Consider the network below: (a) Write down the adjacency matrix for the given netw0rk using the formula. 1, if nodes 2' and j are connected by an edge A = [as]: at\": = . 01 otherWISe. Index your rows and columns in the order s, a, b, c, d, e, f, t. (b) Without doing any matrix multiplication, write down the top row of A2, and explain your reasoning. (c) Draw a tree, with root 5, indicating the shortest path from s to all the other nodes. Use the BFS method from class. (d) Using the data in your tree, employ the recursive algorithm from class to compute the number of shortest paths from s to t. (e) Without doing any matrix multiplication, state and explain the entry in the row of node 3 and the column of node 15 in A3. 3. The vertex chromatic number of a graph is the minimum number of colours needed to colour the vertices of the graph so that no pair of adjacent vertices share the same colour. (a) For the graph of Q2, nd upper and lower bounds on the vertex chromatic number. Explain your reasoning and name any theorems used. (b) Find a minimum colouring for the graph of Q2

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