Semidirect product constructions of directed strongly regular graphs

Duval, Art M.; Iourinski, Dmitri

doi:10.1016/s0097-3165(03)00141-9

Cited by 22 publications

(60 citation statements)

References 3 publications

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“…The main difference in our approach is that we focus our construction in the existence of an appropriate group of automorphisms. Duval and Iourinski pointed out also in the direction of obtaining DSRG with given groups of automorphisms in [4], where they found a family of DSRGs that were also Cayley digraphs and that fits with the particular case of our parameters when d = 1. The digraphs obtained by Duval and Iourinski have the nice property that, when interpreted as difference digraphs, they correspond to subgroups of index 1, that is, their difference number is 1, while in our construction the index of the subgroup is de.…”

Section: Proposition 32 a Family {S X Y } Of Subsets Of A Group G Ismentioning

confidence: 57%

New tools for the construction of directed strongly regular graphs: Difference digraphs and partial sum families

Martínez

Araluze

2010

Journal of Combinatorial Theory, Series B

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We define a class of digraphs involving differences in a group that generalizes Cayley digraphs, that we call difference digraphs. We define also a new combinatorial structure, called partial sum family, or PSF for short, from which we obtain difference digraphs that are directed strongly regular graphs. We give an infinite family of PSFs and we give also twelve sporadic ones that generate directed strongly regular graphs whose existence was previously undecided.

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Section: Proposition 32 a Family {S X Y } Of Subsets Of A Group G Ismentioning

confidence: 57%

New tools for the construction of directed strongly regular graphs: Difference digraphs and partial sum families

Martínez

Araluze

2010

Journal of Combinatorial Theory, Series B

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“…The graphs constructed recently by Duval and Iourinski in [3] have adjacency matrices of the form given in Theorem 6.8 (with d = 1).…”

Section: Matrix Constructionsmentioning

confidence: 99%

“…Interest in these graphs was recently revived by Klin, Munemasa, Muzychuk, and Zieschang [9], and there have been a number of recent papers ( [3], [4], [6], [7], [8]). …”

Section: Introductionmentioning

confidence: 99%

Strongly regular graphs

Godsil¹,

Meagher²

2015

Erdős–Ko–Rado Theorems: Algebraic Approaches

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Acknowledgment: The second and third authors would like to thank the department of Combinatorics and Optimization at the University of Waterloo for their hospitality during the initial research for this paper. AbstractWe develop a theory of representations in R m for directed strongly regular graphs, which gives a new proof of a nonexistence condition of Jørgensen [8]. We also describe some new constructions.

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“…Numerous papers have been published on the subject of DSRGs (see, for example, [5,6,8,[11][12][13][14]16,24]). In 1997 Klin, Munemasa, Muzychuk and Zieschang [15] proved that a DSRG cannot be a Cayley digraph of an abelian group, whereas in 1999, Hobart and Shaw [11] gave constructions of DSRGs which are Cayley digraphs of nonabelian groups.…”

mentioning

confidence: 99%

“…In 2002 Fiedler, Klin and Muzychuk [8] determined DSRGs of order v 20 having a vertex-transitive automorphism group, which combined together with results in [12] gives a complete answer to Duval's question posed in [5] about the existence of DSRGs of order v 20. Further examples of Cayley digraphs which are DSRGs were given in 2003 by Duval and Iourinski [6]. In 2004 Klin, Munemasa, Muzychuk and Zieschang [16] studied DSRGs with the aid of coherent algebras, and constructed new infinite families of DSRGs.…”

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confidence: 99%

Partial sum quadruples and bi-Abelian digraphs

Araluze

Kovács

Kutnar

et al. 2012

Journal of Combinatorial Theory, Series A

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As a generalization of undirected strongly regular graphs, a digraph X without loops, of valency k and order v is said to be a (v, k, μ, λ,t)-directed strongly regular graph whenever for any vertex u of X there are t undirected edges having u as an endvertex and for every two different vertices u and w of X the number of paths of length 2 starting at u and ending at w is λ or μ depending only on whether uw is an arc of X or not. An m-Cayley digraph of a group H is a digraph admitting a semiregular group of automorphisms having m orbits, all of equal length, isomorphic to H. In this paper, the structure of directed strongly regular 2-Cayley graphs of cyclic groups is investigated. In particular, the arithmetic conditions on parameters v, k, μ, λ, and t are given.Also, several infinite families of directed strongly regular graphs which are also 2-Cayley digraphs of abelian groups are constructed.

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Semidirect product constructions of directed strongly regular graphs

Cited by 22 publications

References 3 publications

New tools for the construction of directed strongly regular graphs: Difference digraphs and partial sum families

New tools for the construction of directed strongly regular graphs: Difference digraphs and partial sum families

Strongly regular graphs

Partial sum quadruples and bi-Abelian digraphs

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