General position problem of hyper tree and shuffle hyper tree networks

Abstract

The general position problem of a graph G is to find a set S of maximum number of vertices in G, such that no three vertices lie on an isometric path in G. The gp-number of G is the cardinality of such a set S in G. The general position problem has numerous applications and one such application is the study of navigation of a robot through graph- structures. The general position problem is NP-complete [8] and hence it is interesting to find the general position number of various networks. In this paper, we study the general position problem of hyper trees and shuffle hyper trees and we also compute the gp-number of n-level hyper tree and n-level shuffle hyper tree networks.