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Specify the shortest route from node 1 to each of the other nodes in the following network. Show work completely, including all relevant temporary and permanent labels for each node.

[3,1] [6,4] 4 [7,2] [10,6]

[11,5] 2 3 2 [3,1] 5 5 3 3 7 4 2 2 1 2 4 4

6 5 [9,3] 3 [8,5] [4,1]

Note:

Node labels were assigned in the following order:

1. Temporary labels of [3,1], [4,1], and [3,1] assigned to nodes 2, 3, and 4, respectively. 2. Node 2 label made permanent – [3,1]; temporary label of [7,2] assigned to node 5. 3. Node 4 label made permanent – [3,1]; temporary label of [6,4] assigned to node 5. 4. Node 3 label made permanent – [4,1]; temporary label of [9,3] assigned to node 6. 5. Node 5 label made permanent – [6,4]; temporary label of [8,5] assigned to node 6 and temporary label of [11,5] assigned to node 7. 6. Node 6 label made permanent – [8,5]; temporary label of [10,6] assigned to node 7. 7. Node 7 label made permanent – [10,6].

Shortest Routes from Node 1

To Node Shortest Route Total Distance 2 1 → 2 3 3 1 → 3 4 4 1 → 4 3 5 1 → 4 → 5 6 6 1 → 4 → 5 → 6 8 7 1 → 4 → 5 → 6 → 7 10

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