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The table gives the weights of a weighted graph G on vertices U, V, W, X, Y, Z. All the edges appear in the table (so for instance VZ is not an edge in the graph). Edge Weight Edge Weight Edge Weight UX 1 UV 3 UW 5 VX 1 YZ 3 XY 6 WY 1 WX 4 XZ 8 VW 2 WZ 5 UZ 9 i. Use Dijkstra's algorithm to find a minimal path from U to Z. ii. We now consider an graph G' whose vertices and edges are the same as G, but which is not a weighted graph. Sketch a planar diagram of G'. iii. Is it possible to add a new edge to G' and maintain planarity? Justify your answer either with a planar diagram or a proof of non-planarity.

The table gives the weights of a weighted graph G on vertices U, V, W, X, Y, Z. All the edges appear in the table (so for instance VZ is not an edge in the graph). Edge Weight Edge Weight Edge Weight UX 1 UV 3 UW 5 VX 1 YZ 3 XY 6 WY 1 WX 4 XZ 8 VW 2 WZ 5 UZ 9 i. Use Dijkstra's algorithm to find a minimal path from U to Z. ii. We now consider an graph G' whose vertices and edges are the same as G, but which is not a weighted graph. Sketch a planar diagram of G'. iii. Is it possible to add a new edge to G' and maintain planarity? Justify your answer either with a planar diagram or a proof of non-planarity.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The table gives the weights of a weighted graph G on vertices U, V, W, X, Y, Z. All the edges appear in the table (so for instance VZ is not an edge in the graph). Edge Weight Edge Weight Edge Weight UX 1 UV 3 UW 5 VX 1 YZ 3 XY 6 WY 1 WX 4 XZ 8 VW 2 WZ 5 UZ 9 i. Use Dijkstra's algorithm to find a minimal path from U to Z. ii. We now consider an graph G' whose vertices and edges are the same as G, but which is not a weighted graph. Sketch a planar diagram of G'. iii. Is it possible to add a new edge to G' and maintain planarity? Justify your answer either with a planar diagram or a proof of non-planarity.
Transcribed Image Text:The table gives the weights of a weighted graph G on vertices U, V, W, X, Y, Z. All the edges appear in the table (so for instance VZ is not an edge in the graph). Edge Weight Edge Weight Edge Weight UX 1 UV 3 UW 5 VX 1 YZ 3 XY 6 WY 1 WX 4 XZ 8 VW 2 WZ 5 UZ 9 i. Use Dijkstra's algorithm to find a minimal path from U to Z. ii. We now consider an graph G' whose vertices and edges are the same as G, but which is not a weighted graph. Sketch a planar diagram of G'. iii. Is it possible to add a new edge to G' and maintain planarity? Justify your answer either with a planar diagram or a proof of non-planarity.
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