Question

8. Nick wants to visit some friend. Graph below represents distance to his friends. c. Nick decides to go visit Bob. Given the following additional data about the number of stations it takes to travel between each friend's house, use Dijks- tra's algorithm to find the shortest path from Nick' to the Bob' house. When answering this question you must show every step in your calculations, in- cluding your final fully-labelled graph. Nick Fil L e ? William Marta stations 2 edge stations edge stations edge stations edge e1 18 e59e9 7 13 9 e6 5 10 7 e 14 e3 8 e7 8 11 5 e4 2 eg 10 e12 9 ez Mark John Anna Bob a. Create the adjacency matrix for this graph, based on an appropriate ordering of the vertex set V. Hint: This may be easier if you re-label your vertices, for example: a Nick b William c Mark d Anna e Fil f Marta g John h Bob b. How many paths of length 4 exist from vertex n to vertex m in the above graph, where n and m are any two vertices in V?

Answer 1

18 15280 WEDNESDAY DAY 296-069 19 & Adjaceney matrix of the graph is given by - To । । ० | 0 0 0 | | 0 | | | 0 0 0 | 0 | ० ० । । । | 0 | 0 0 10 | | 0 | 0 | 0 100 । 0 0 | 0 । 000 | 0 0 0 ज ___ A ५ २ | 2 | | 2 । । । । 6 2 2 । ० 5 0 4 202 0 0 2 2 0 ५ ७ ५ ० ।। 2 । । 0 । 0 । 2 । ० । । । । ० 2 ___R । 07 A | 29 Bo 23 24 1 33 1467 29883 24 293 14 8 2032 5 10 15 5 20 2५ 26 125 10 26 16 2 18 28 ५६ 8 39 2५ ५ । | 33 २५ 32 265 ५० । ।। 18 24 18 18 16 12 ५ | 6 8 20 2 5 ॥ । 10 The secret of success is to know something no one else knows

19 Wechat THURUDI the no of paths of length 4 from vester in to vortex mo is the b a nm the entry of the wall min Ah e.g there are 29 many path from vestes a toa,