Question: Let G be a connected plane graph with v vertices and e edges so that every vertex lies on one face of size 4, one

Let G be a connected plane graph with v vertices and

Let G be a connected plane graph with v vertices and e edges so that every vertex lies on one face of size 4, one face of size 6, and one face of size 8. Let fa, f6, fs be the number of faces of size 4, 6, 8 (respectively) (i) Express e in terms of v (Hint: how many edges are incident with each vertex?) (ii) Express f4, f6, and fs in terms of v (iii) Use (i) and (ii) to determine v (iv) Determine e, fa, f6, and fs Construct a plane graph with the parameters Let G be a connected plane graph with v vertices and e edges so that every vertex lies on one face of size 4, one face of size 6, and one face of size 8. Let fa, f6, fs be the number of faces of size 4, 6, 8 (respectively) (i) Express e in terms of v (Hint: how many edges are incident with each vertex?) (ii) Express f4, f6, and fs in terms of v (iii) Use (i) and (ii) to determine v (iv) Determine e, fa, f6, and fs Construct a plane graph with the parameters

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