Article ID Journal Published Year Pages File Type
4598586 Linear Algebra and its Applications 2016 14 Pages PDF
Abstract

Denote the scrambling index set of primitive minimally strong digraphs of order n   by SInSIn. For n≥13n≥13, we show that SInSIn contains all integers in the interval [3,K1(n)][3,K1(n)], whereK1(n)={n2+12n−138,if both n and n+12 are odd,n2+12n−58,if n is odd and n+12 is even,n2+10n−168,if n is even and n2 is odd,n2+10n−88,if both n and n2 are even. We also identify all elements of SInSIn which are larger than (n2−6n+13)/2(n2−6n+13)/2 (n   is odd) or (n2−6n+12)/2(n2−6n+12)/2 (n   is even). It is shown that there exist more “gaps” in the set SInSIn.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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