“…The 1-skeleton of a polytope P is the graph whose vertex set is the vertex set of P and edge set is the set of geometric edges or one-dimensional faces of P . The study of 1-skeleton is of interest, since, on the one hand, there are algorithms for perfect matching, set covering, independent set, a ranking of objects, problems with fuzzy measures, and many others that are based on the vertex adjacency relation in 1-skeleton and the local search technique (see, for example, [1,6,11,12,15]). On the other hand, some characteristics of 1-skeleton, such as the diameter and clique number, estimate the time complexity for different computation models and classes of algorithms [7,9,18].…”