Automorphism groups of DRADs

Itô, Noboru; Cheng, Kai N.; Leong, Yu K.

doi:10.1515/9783110848397-011

Cited by 9 publications

(7 citation statements)

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“…This gives a normally regular digraph with parameters (39, 14,4,7). In this particular case, the normally regular digraph is isomorphic to the graph constructed in Corollary 37, with (s, t) = (0, 3).…”

Section: Construction From Desarguesian Planesmentioning

confidence: 94%

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Normally Regular Digraphs

Jørgensen

2015

Electron. J. Combin.

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A normally regular digraph with parameters (v, k, λ, µ) is a directed graph on v vertices whose adjacency matrix A satisfies theThis means that every vertex has out-degree k, a pair of non-adjacent vertices have µ common out-neighbours, a pair of vertices connected by an edge in one direction have λ common out-neighbours and a pair of vertices connected by edges in both directions have 2λ − µ common out-neighbours. We often assume that two vertices can not be connected in both directions.We prove that the adjacency matrix of a normally regular digraph is normal. A connected k-regular digraph with normal adjacency matrix is a normally regular digraph if and only if all eigenvalues other than k are on one circle in the complex plane. We prove a Bruck-Ryser type condition for existence and give a combinatorial proof for a restriction excluding existence in some cases with small values of λ. There is a structural characterization of normally regular digraphs with µ = 0 or µ = k. For other values of µ we give several constructions of normally regular digraphs. In many cases these graphs are Cayley graphs of abelian groups and the construction is then based on a generalization of difference sets. In particular, if 4t + 1, 4s + 3 and q are prime powers and r is not divisible by 3 we get normally

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Section: Construction From Desarguesian Planesmentioning

confidence: 94%

“…Asymmetric normally regular digraphs with µ = λ have been studied by Ito [13], [14], [15], [16] and [17], and also by Ionin and Kharaghani [12].…”

Section: Introductionmentioning

confidence: 99%

Normally Regular Digraphs

Jørgensen

2015

Electron. J. Combin.

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“…By [6], it suffices to check only the nearly triple regularity. Further, by Proposition in w we have only to show that the three-block intersection numbers of D~+ 1 and D~+I are equal to 2m2--m and 2m 2 -2m.…”

Section: Constructionmentioning

confidence: 99%

“…These properties of Fjustifies our calling ofFa DRAD. For some basic results on DRAD's see [5,6,7,8].…”

Section: Introductionmentioning

confidence: 99%

Nearly triply regular Drad’s ofRH type

Itô

Raposa

1992

Graphs and Combinatorics

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“…The term DRAD comes from the equivalence between these types of difference sets to doubly regular asymmetric digraphs [6]. These types of difference sets also give rise to nonsymmetric imprimitive association schemes.…”

Section: Introductionmentioning

confidence: 99%

Reversible and DRAD difference sets in

Webster

2011

J of Combinatorial Designs

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Abstract:The existence of Hadamard difference sets has been a central question in design theory. Reversible difference sets have been studied extensively. Dillon gave a method for finding reversible difference sets in groups of the form (C 2 r ) 2 . DRAD difference sets are a newer concept. Davis and Polhill showed the existence of DRAD difference sets in the same groups as Dillon. This article determines the existence of reversible and DRAD difference sets in groups of the form (C 2 2r ) 3 . These are the only abelian 2-groups outside of direct products of C 4 and (C 2 r ) 2 known to contain reversible and DRAD difference sets. q 2011

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Automorphism groups of DRADs

Cited by 9 publications

References 0 publications

Normally Regular Digraphs

Normally Regular Digraphs

Nearly triply regular Drad’s ofRH type

Reversible and DRAD difference sets in

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