Question: Subject - Graph Theory, Discrete Math (a) Let G = (V, E) be a connected planar graph such that |V | = 16 and every

Subject - Graph Theory, Discrete Math

(a) Let G = (V, E) be a connected planar graph such that |V | = 16 and every vertex has degree 4. It is embedded in the plane so that every region is either a triangle or a quadrangle. How many triangles and how many quadrangles does this embedding have? Justify your answer.

(b) Let G be a planar connected graph. Prove that G has at least one vertex of degree 5.

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