Super-simple 2-(v; 5; 1) directed designs and their smallest defining sets

Nasrin Soltankhah; Farzane Amirzade

Super-simple 2-(v; 5; 1) directed designs and their smallest defining sets

Combinatorics 2012-07-10 v2

Authors: Nasrin Soltankhah , Farzane Amirzade

Abstract

In this paper we investigate the spectrum of super-simple 2- $(v,5,1)$ directed designs (or simply super-simple 2- $(v,5,1)$ DDs) and also the size of their smallest defining sets. We show that for all $v\equiv1,5\ ({\rm mod}\ 10)$ except $v=5,15$ there exists a super-simple $(v,5,1)DD$ . Also for these parameters, except possibly $v=11,91$ , there exists a super-simple 2- $(v,5,1)$ DD whose smallest defining sets have at least a half of the blocks.

Keywords

combinatorial designs

Cite

@article{arxiv.1205.6047,
  title  = {Super-simple 2-(v; 5; 1) directed designs and their smallest defining sets},
  author = {Nasrin Soltankhah and Farzane Amirzade},
  journal= {arXiv preprint arXiv:1205.6047},
  year   = {2012}
}

Comments

accepted in Australas. J. of Combin. arXiv admin note: text overlap with arXiv:1205.6395

Super-simple 2-(v; 5; 1) directed designs and their smallest defining sets

Abstract

Keywords

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