- #1
Natasha1
- 493
- 9
I wondered if someone could help me with the following problem.
Gn (n >= 2) is a graph representing the vertices abd edges of a regular 2n sided polygon, with additional edges formed by the diagonals for each vertex joined to the vertex opposite i.e. vertex 1 is joined to n+1, vertex 2 to n+2 and so on, vertex n to 2n.
1) How can I show that G3 is isomorphic to K3,3?
2) How can I state (with reason) a value of n for which Gn is planar. Explaining why for all values greater than this value of n, Gn will be non-planar?
![Frown :frown: :frown:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Gn (n >= 2) is a graph representing the vertices abd edges of a regular 2n sided polygon, with additional edges formed by the diagonals for each vertex joined to the vertex opposite i.e. vertex 1 is joined to n+1, vertex 2 to n+2 and so on, vertex n to 2n.
1) How can I show that G3 is isomorphic to K3,3?
2) How can I state (with reason) a value of n for which Gn is planar. Explaining why for all values greater than this value of n, Gn will be non-planar?