Question

5. i) Find the cost adjacency matrix for the graph given below.

Answer 1

Adjacency Matrix:

A B C AO 15 3 B 15 0 4 3 4 1 DO 2 3 s 7 0 8 TO 5 0 D 0 2 3 0 0 2 S 7 0 8 0 0 0 T 0 5 0 2 0 0

DETAILS:

Arrange the nodes in the same order for rows and for columns of the matrix.

Fill the matrix with weights between two nodes (row and column)

For instance, the weight between node A and C is 3 so row A and column C meet at a value 3.

Since this is an un-directed graph (no directions between nodes), the adjacency matrix is expected to be symmetrical so row C and column A will also meet at a value 3.

If two nodes are not connected together, record the weight as zero (0).

The loop with weight of 1 on node C mean that node C is re-connecting to itself so in the matrix, row C and column C meet at a value 1.

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A B C AO 15 3 B 15 0 4 3 4 1 DO 2 3 s 7 0 8 TO 5 0 D 0 2 3 0 0 2 S 7 0 8 0 0 0 T 0 5 0 2 0 0