Isometric Path Partition Problem on Tree Derived Architectures

Abstract

Abstract An isometric path partition of a graph G is defined as a set of isometric paths that partition the vertex set of G. The problem of isometric path partition is to obtain a minimum isometric path partition of G. The isometric path partition number of a graph G, denoted by ip p (G) is the minimum cardinality of isometric path partition in G. In this paper, we compute the isometric path partition number of certain tree derived architectures like hypertrees, 1-rooted sibling trees, k-rooted sibling trees, l-complete binary trees, and l-sibling trees.