The Bipanconnectivity and Hamiltonian-Connectivity of Enhanced Hypercube

Abstract

Enhanced hypercube $Q_{n,k}$ is one of the attractive variant of hypercube. In this paper, we show that the $n$-dimensional enhanced hypercube is bipanconnected when $n$ and $k$ have the same parity. We also show that the $n$-dimensional enhanced hypercube is Hamiltonian-connected when $n$ and $k$ have the different parity.