General Position Problem of Butterfly Networks

Abstract: A general position set S is a set S of vertices in G(V,E) such that no three vertices of S lie on a shortest path in G. Such a set of maximum size in G is called a gpset of G and its cardinality is called the gp-number of G denoted by gp(G). The authors who introduced the general position problem stated that the general position problem for butterfly networks was open. A well-known technique to solve the general position problem for a given network is to use its isometric path cover number as an upper bound. The general position problem for butterfly networks remained open because this technique is not applicable for butterfly networks. In this paper, we adopt a new technique which uses the isometric cycle cover number as its upper bound. This technique is interesting and useful because it opens new avenues to solve the general position problem for networks which do not have solutions yet.