On the Connectivity of the Vietoris-Rips Complex of a Hypercube Graph
Combinatorics
2023-11-14 v1 Algebraic Topology
Abstract
We bring in the techniques of independence complexes and the notion of total dominating sets of a graph to bear on the question of the connectivity of the Vietoris-Rips complexes of an -hypercube graph. We obtain a lower bound for the connectivity of for an arbitrary -dimension hypercube and at all scale parameters . The obtained bounds disprove the conjecture of Shukla that is -connected.
Keywords
Cite
@article{arxiv.2311.06407,
title = {On the Connectivity of the Vietoris-Rips Complex of a Hypercube Graph},
author = {Martin Bendersky and Jelena Grbic},
journal= {arXiv preprint arXiv:2311.06407},
year = {2023}
}