Question

014) Draw a dual graph G for the following planar map, and find a coloring for the vertices of G that uses x(G) number of colors o cean Q15. Solve the following TSP problem 3 4 55305 302 320 C Using the nearest neighbor algorithm., if A is the home city. Shade the edges used. Find the distance travelled. E x piaun the qlgor tam a) 340 305 30 D 320 С Using the sorted edge algorithm. Show work ( sort the miles on the egdes) and shade on the route. Find the the edges b) lyo ritm distance travelled. xplan the a 340 0 3626 3 20 C

Answer 1

500 90 b 302 305 3 20 starting -Arom2 nearest vertice starting from. Aケnearest vertex is D The first parth is AD From D the nearest vertex is C The second path is Dc CAS-CB too-Path Erom.e-ナwe have

rom ey we have two path CA CB ー-but-we-cam- cross.. each.-vertex- once We want consider CA ser Third Path is CB Agai n the nearest path-is. EB Now all the vertices are covered So we can go back to A Last path is EA The path is A-DC B-A Distance-is-i 355 wnif ( add- ATT the tenrw ot the edges)

g1s b 500 20 4.0 30 2 30 D 32 0 First we write all the udges with dis tances-ranging-from min to max . ЕС 165 ED 3 0 2 BD-350 AC 2O DC32 0 AE 205 EB 340 The only-一care. that, should-be-tanen - in this algorithm is 3 edges shauld not mett ane veriex and na circuct shaud be formed without all the Vert i

and A c We cant because at. A there ED Would also generate a cycle same with Bc ur path is OLA as fallovos