1Prove the Heawood graph is nonplanar by using Kuratowskis T

1)Prove the Heawood graph is non-planar by using Kuratowski\'s Theorem and

2)what is the genus of the Heawood Graph

Solution

1)Headwood graph has vertices=14,chromatic number=2,chromatic index=3,edges=21,radius=3,girth=6

By kuratowdki\'s theorem,the edges are crossing each other.we know that,a planar graph has edges without crossing.so,it is non planar as like k5 and k(3,3)

2)genus=1