The number of equivalence classes of symmetric sign patterns

This paper shows that the number of sign patterns of totally non-zero symmetric n-by-n matrices, up to conjugation by monomial matrices and negation, is equal to the number of unlabelled graphs on n vertices. Key words: symmetric matrix, sign pattern, enumeration, duality

• Type: Journal
• Year: 2006
• Where: DM
• Authors: Peter J. Cameron, Charles R. Johnson
• Keywords: DM 2006, Monomial Matrices, Sign Pattern, Symmetric N-by-n Matrices