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We bring in the techniques of independence complexes and the notion of totaldominating sets of a graph to bear on the question of the connectivity of theVietoris-Rips complexes $VR(Q_n; r)$ of an $n$-hypercube graph. We obtain alower bound for the connectivity of $VR(Q_n; r)$ for an arbitrary $n$-dimensionhypercube and at all scale parameters $r$. The obtained bounds disprove theconjecture of Shukla that $\VR$ is $r$-connected.

On the Connectivity of the Vietoris-Rips Complex of a Hypercube Graph