Isometric Path Partition Number of Butterfly Network and X–Trees

Abstract

Abstract A set S of isometric paths that partition the vertex set of a graph G is called an isometric path partition of G. The isometric path partition number of G is the minimum cardinality of such a set S in G. It is denoted by ipp(G). The isometric path partition problem is to find a minimum isometric path partition of a given graph G. The isometric path partition problem has wide applications in the designing of an efficient algorithm in many architectures. The problem of determining the isometric path partition of a given graph G is NP-complete and hence it is interesting to compute the exact value of isometric path partition of different networks. In this paper, we study the isometric path partition problem of butterfly networks, complete binary trees, rooted complete binary trees, X–trees and compute the isometric path partition number of these graphs.