Designs, Codes and Cryptography

, Volume 84, Issue 1–2, pp 283–294 | Cite as

The Smith group of the hypercube graph

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Abstract

The n-cube graph is the graph on the vertex set of n-tuples of 0s and 1s, with two vertices joined by an edge if and only if the n-tuples differ in exactly one component. We compute the Smith group of this graph, or, equivalently, the elementary divisors of an adjacency matrix of the graph.

Keywords

Hypercube Association scheme Smith normal form 

Mathematics Subject Classification

05E30 
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Notes

Acknowledgments

This work was partially supported by a Grant from the Simons Foundation (#204181 to Peter Sin). The work of the third author (Qing Xiang) was partially supported by an NSF grant, DMS-1600850.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.NewarkUSA
  2. 2.Department of MathematicsUniversity of FloridaGainesvilleUSA
  3. 3.Department of Mathematical SciencesUniversity of DelawareNewarkUSA

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