A directed graph version of strongly regular graphs

Duval, Art M.

doi:10.1016/0097-3165(88)90043-x

Cited by 93 publications

(155 citation statements)

References 10 publications

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“…We have already shown (1) and (2). The equations (3) and (4) follow from A = P DP −1 and the definitions of E 0 , E 1 , E 2 .…”

Section: Representationsmentioning

confidence: 99%

“…Duval [2] gave a list of feasible parameter sets with v ≤ 20 which pass all parameter conditions given in that paper. This list has been extended to v ≤ 110 by Hobart and Brouwer and is available on the web [1], with notes giving the current knowledge about existence.…”

Section: Theorem (Duval [2]) Letmentioning

confidence: 99%

“…Directed strongly regular graphs are directed versions of strongly regular graphs, and were originally defined by Duval [2]. Many results for strongly regular graphs have analogues for the directed version; in particular the eigenvalues are strikingly similar.…”

Section: Introductionmentioning

confidence: 99%

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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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“…We have already shown (1) and (2). The equations (3) and (4) follow from A = P DP −1 and the definitions of E 0 , E 1 , E 2 .…”

Section: Representationsmentioning

confidence: 99%

Section: Theorem (Duval [2]) Letmentioning

confidence: 99%

See 1 more Smart Citation

Strongly regular graphs

Godsil¹,

Meagher²

2015

Erdős–Ko–Rado Theorems: Algebraic Approaches

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“…Then SRGs admitting semiregular groups of automorphisms with three orbits were studied by Kutnar, Marušič, Miklavič andŠparl [6]. Recently, Martínez and Araluze [11] studied this question for an arbitrary number of orbits and for directed SRGs, introduced by Duval in [5]. They translated the problem into the language of the so-called partial sum families (see also [1,2]).…”

Section: Introductionmentioning

confidence: 99%

QUASI m-CAYLEY STRONGLY REGULAR GRAPHS

Kutnar¹,

Malnič²,

Martínez³

et al. 2013

Journal of the Korean Mathematical Society

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Abstract. We introduce a new class of graphs, called quasi m-Cayley graphs, having good symmetry properties, in the sense that they admit a group of automorphisms G that fixes a vertex of the graph and acts semiregularly on the other vertices. We determine when these graphs are strongly regular, and this leads us to define a new algebro-combinatorial structure, called quasi-partial difference family, or QPDF for short. We give several infinite families and sporadic examples of QPDFs. We also study several properties of QPDFs and determine, under several conditions, the form of the parameters of QPDFs when the group G is cyclic.

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“…Directed Strongly Regular Graphs (DSRG) were introduced by Duval as a generalization of strongly regular graphs (SRG's) [4]. As observed in [8] a special case of these are the doubly regular tournaments or equivalently, the skew Hadamard matrices.…”

Section: Introductionmentioning

confidence: 99%