Connectivity and edge-bipancyclicity of hamming shell

TL;DR

This paper proves that Hamming shells, derived from n-cubes by deleting Hamming codes, are edge-bipancyclic and highly connected, extending their known properties.

Contribution

It establishes that Hamming shells are edge-bipancyclic and (n-1)-connected, adding new insights into their cycle structure and connectivity.

Findings

Hamming shells are edge-bipancyclic.

Hamming shells are (n-1)-connected.

Hamming shells retain Hamiltonian and connectivity properties.

Abstract

An Any graph obtained by deleting a Hamming code of length n 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. Moreover, it is Hamiltonian and connected. In this paper, we prove that a Hamming shell is edge-bipancyclic and (n-1)-connected.