7. 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 (and no other faces). Let $4, 56, fo be the number of faces of size 4, 6, 8 (respectively). (i) Express e in terms of v (ii) Express fa, fe, and fs in terms of v (iii) Use (i) and (ii) to determine v (iv) Determine e, f4, f6, and fs. (v) Draw such a graph G. 7. 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 (and no other faces). Let $4, 56, fo be the number of faces of size 4, 6, 8 (respectively). (i) Express e in terms of v (ii) Express fa, fe, and fs in terms of v (iii) Use (i) and (ii) to determine v (iv) Determine e, f4, f6, and fs. (v) Draw such a graph G