General Position Problem of Butterfly Derived Architectures

The problem of finding a largest general position set S of G in which no three vertices lie on an isometric path is referred as the general position problem. This set S is called a gp-set of G. The gp-number, denoted by gp(G) is the cardinality of S in G. This NP-complete problem is one of the recent topic of research which has wide applications in navigation of autonomous robots [13]. Butterfly network is one of the most significant and widely researched interconnection architecture. Previously, we have studied the general position problem of butterfly network [22]. In this article, we solve the general position problem of butterfly derived architectures such as augmented butterfly network, enhanced butterfly network and compute their gp-number.