The exponent set of symmetric primitive (0, 1) matrices with zero trace

Bolian Liu, Brendan D. McKay, Nicholas C. Wormald, Zhang Ke Min

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Abstract

We prove that the exponent set of symmetric primitive (0, 1) matrices with zero trace (the adjacency matrices of the simple graphs) is {2,3,...,2n-4}{minus 45 degree rule}S, where S is the set of all odd numbers in {n-2,n-1,...,2n-5}. We also obtain a characterization of the symmetric primitive matrices with zero trace whose exponents attain the upper bound 2n-4.

Original languageEnglish
Pages (from-to)121-131
Number of pages11
JournalLinear Algebra and Its Applications
Volume133
Issue numberC
DOIs
Publication statusPublished - 1990
Externally publishedYes

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