The 3- Rainbow Index of Hypercube and Hypertree Networks

Abstract

A path P in an edge coloured graph with no two edges sharing the same colour is called a
rainbow path. A tree T in G is a rainbow tree if no edges of T receive the same colour. For a
vertex subset S ⊆ V(G), a tree that connects S in G is called an S - tree. The minimum number
of colours that are needed in an edge-colouring of G such that there is a rainbow S- tree for
each k-subset S of V(G) is called the k − rainbow index of G, denoted by rxk(G). In this paper,
we have computed the 3- rainbow index of Hypercube and Hypertree networks.