Suppose a connected planar graph P has every vertex of degre

Solution

solution : No, let \' e\' denote the edges of planer Graph P and \'f\' denotes the face of planner graph .then if every face has degree at least 3 then 2e>=3f   -------( 1) .

if every vertex has degree at least 3 then 2e>=3v --------(2).

by (1) and (2) we get 3e >= 3(f+v) .

here vertex degree at least 3.and face size at least 3

therefore 3e >=3(3+3)

= 3e>=18

= e>=6 . implise that planner Graph has at least 6 edges.