Question: (a) Let G=(V,E) be connected planar graph with V=n3 and deg(v)>1 for every vV such that every its region is bounded by 3 edges. Prove

(a) Let G=(V,E) be connected planar graph with V=n3 and deg(v)>1

(a) Let G=(V,E) be connected planar graph with V=n3 and deg(v)>1 for every vV such that every its region is bounded by 3 edges. Prove that G has exactly 2n4 regions and E=3n6. (b) Let G=(V,E) be simple planar graph with V4. Prove that G has 4 vertices whose degree does not exceed 5

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