Rainbow colouring of Oxide Networks

Abstract

A path in an edge coloured graph with no two edges sharing the same colour is called a rainbow path. The rainbow connection number $rc(G)$ of $G$ is the minimum integer $k$ for which there exists an $k-$ edge-coloring of $G$ such that every two distinct vertices of $G$ are connected by a rainbow path. It is known that computing the rainbow connection number of a graph is $NP-$Hard. So, it is interesting to compute $rc(G)$ for any given graph $G$. In this paper, we compute the rainbow connection number for oxide networks.