Let G be a connecteed plannar graph with 100 vertices that i

Let G be a connecteed plannar graph with 100 vertices that is cubic (every vertex has desgree exactly 3). How many vertices does the dual graph G* have?

Solution

let no. of edge in graph G=m

let no. of verices in graph G=n=100

let no. of faces in graph G=f=6

n - m + f = 2

m=104

If G is a connected planar graph with n vertices, f faces and m edges, then G* has f vertices, n faces and m edges.

so, dual graph G* have 104 vertices.