suppose a connected planar graph P has every vertex of degre

suppose a connected planar graph P has every vertex of degree at least 3 and every face of size at least 3. Can P have fewer than six edges? Show work please

Solution

AS the graph P has every vertex of degree atleast 3, it has 3-dimensional figure and each vertev has the coordinate to be (x,y,z). A cubiod is 3 dimensional with 2*2*2 = 8 vertices or edges. If it is cut diagonally it can have 6 edges. Under no circumstances, it can have less than 6 edges.