... L(a) the link of a restricted to S. Let x1,x2, ,x7denote the sizes of the links of the vertices of F restricted to S with x1≤ x2≤···≤x7≤ 28. The solutions (y1,y2, ,y7) of the ... ∈ V (G), the link LS(a)ofa restricted to a subset S of V (G)is{{b, c} : {a, b, c}∈E(G),b,c ∈ S}. The proof of the next result is technical and it is presented in the nextsection.Theorem 3.1. ... (27,27,27,27,28,28,28)Then (x1,x2, ,x7) is one of the 7-tuples above. The following result is folklore and itwill be used in the proof of our theorem. the electronic journal of combinatorics 11 (2004), #N3...