TY - JOUR

T1 - The exponent set of symmetric primitive (0, 1) matrices with zero trace

AU - Liu, Bolian

AU - McKay, Brendan D.

AU - Wormald, Nicholas C.

AU - Min, Zhang Ke

PY - 1990

Y1 - 1990

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0040875412&partnerID=8YFLogxK

U2 - 10.1016/0024-3795(90)90244-7

DO - 10.1016/0024-3795(90)90244-7

M3 - Article

AN - SCOPUS:0040875412

SN - 0024-3795

VL - 133

SP - 121

EP - 131

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - C

ER -