The number of equivalence classes of symmetric sign patterns

Peter J. Cameron*, Charles R. Johnson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


This paper shows that the number of sign patterns of totally non-zero symmetric n-by-n matrices, up to conjugation by permutation and signature matrices and negation, is equal to the number of unlabelled graphs on n vertices.

Original languageEnglish
Pages (from-to)3074-3077
Number of pages4
JournalDiscrete Mathematics
Issue number23 SPEC. ISS.
Publication statusPublished - 6 Dec 2006


  • Duality
  • Enumeration
  • Sign pattern
  • Symmetric matrix


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