Connectivity and edge-bipancyclicity of Hamming shell

Abstract

An Any graph obtained by deleting a Hamming code of length n = 2 r − 1 from a n−cube Qn is called as a Hamming shell. It is well known that a Hamming shell is vertex-transitive, edge-transitive, distance preserving [1,2,3,4]. Moreover, it is Hamiltonian[6] and connected [5] . In this paper, we prove that a Hamming shell is edge-bipancyclic and (n − 1)−connected.