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Doubly regular asymmetric digraphs

1988
*
Discrete Mathematics
*

Namely D is

doi:10.1016/0012-365x(88)90208-7
fatcat:sh2mc77g5bg6raomxxlpc5bn7y
*regular*of valency k and*doubly**regular*of double valency A. 2 . 0 Proposition 5 . 205 Some basic properties of DRADs Proposition 1. v 2 2k + 1 and hence k 2 2A. + 1. Proof. ... Now we define a*digraph*D = (V, A), where V and A denote the sets of vertices and arcs respectively, as follows: V = P, and (a, b) is an arc if and only if b E T-'(a). ...##
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Normally Regular Digraphs
[article]

2014
*
arXiv
*
pre-print

A connected k-

arXiv:1410.8424v1
fatcat:uqlghdruxjbarlw5kddy2wjvze
*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 that the adjacency matrix of a normally*regular**digraph*is normal. ... Then the Cayley graph Cay(F, Q) is a*doubly**regular*tournament. We conclude this section with two small*asymmetric*normally*regular**digraphs*. ...##
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Hoffman's coclique bound for normal regular digraphs, and nonsymmetric association schemes
[article]

2015
*
arXiv
*
pre-print

We extend Hoffman's coclique bound for

arXiv:1511.07537v1
fatcat:hytvwrastvhtbhhqsxcxlyqcku
*regular**digraphs*with the property that its adjacency matrix is normal, and discuss cocliques attaining the inequality. ... As a consequence, we characterize skew-Bush-type Hadamard matrices in terms of*digraphs*. We present some normal*digraphs*whose vertex set is decomposed into disjoint cocliques attaining the bound. ... We will refer to a*doubly**regular**asymmetric**digraph*with parameters (v, k, λ) as a DRAD(v, k, λ). ...##
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Page 652 of Mathematical Reviews Vol. , Issue 91B
[page]

1991
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Mathematical Reviews
*

Alan Tucker (1-SUNYS-S)
91b:05091 05C25 05B10 05C20 20B25
Ito, Noboru (J-PKNN-AM)

*Doubly**regular**asymmetric**digraphs*with rank 5 automorphism groups. ... In this paper the author classifies certain*doubly**regular**asymmetric*(v,k,A) diagraphs with rank 5 automorphism groups. ...##
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Page 8085 of Mathematical Reviews Vol. , Issue 2003k
[page]

2003
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Mathematical Reviews
*

T is

*asymmetric*if whenever (x, y) is an arc then (y,x) is not an are. A*doubly**regular**asymmetric**digraph*with parameters (v,k, A) is referred to as DRAD(v,k,A). ... .]; however this question is still open.” 2003k:05059 05C20 05B05 lonin, Yury J. (1-CMI; Mount Pleasant, MI); Kharaghani, Hadi (3-LETH; Lethbridge, AB)*Doubly**regular**digraphs*and symmetric designs. ...##
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When does a digraph admit a doubly stochastic adjacency matrix?

2010
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Proceedings of the 2010 American Control Conference
*

In this paper, we fully characterize the class of

doi:10.1109/acc.2010.5530578
fatcat:caxesolag5a5nfepkz6z2pgwki
*digraphs*that admit an edge weight assignment that makes the*digraph*adjacency matrix*doubly*stochastic. ...*Digraphs*with*doubly*stochastic adjacency matrices play an essential role in a variety of cooperative control problems including distributed averaging, optimization, and gossiping. ... G a C-*regular**digraph*with C < ds(G). ...##
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Page 6172 of Mathematical Reviews Vol. , Issue 90K
[page]

1990
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Mathematical Reviews
*

A

*digraph*DZ = (V,U) of order v is a*doubly**regular**asymmetric*(v,x,A)*digraph*if (i) DM is*regular*of valency k, (ii) D is*doubly**regular*of double valency A, and (iii) D is*asymmetric*. ... Hemminger (1-VDB) 90k:05102 05C50 05C20 Ito, Noboru (J-PKNN-AM) On spectra of*doubly**regular**asymmetric**digraphs*of RH-type. Graphs Combin. 5 (1989), no. 3, 229-234. Let v,x,A be positive integers. ...##
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Doubly regular digraphs and symmetric designs

2003
*
Journal of combinatorial theory. Series A
*

If an incidence matrix N of a symmetric design is such that N þ N t is a ð0; 1Þ matrix, then N is an adjacency matrix of a

doi:10.1016/s0097-3165(02)00015-8
fatcat:gj3wmwsmnnexhb7xtdjt423pzq
*doubly**regular**asymmetric**digraph*, and vice versa. ... We construct several parametrically new infinite families of such*digraphs*. To carry on some of these constructions, we obtain an infinite family of skew balanced generalized weighing matrices. r ... to a*doubly**regular**asymmetric**digraph*with parameters ðv; k; lÞ as a DRADðv; k; lÞ: For further information on these and more general*digraphs*see [9, 11] ...##
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Distributed Strategies for Generating Weight-Balanced and Doubly Stochastic Digraphs

2012
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European Journal of Control
*

We refer to a

doi:10.3166/ejc.18.539-557
fatcat:gjtwtazgrbaqtcstxeyy5zzniy
*digraph*as*doubly*stochasticable (weight-balanceable) if it admits a*doubly*stochastic (weight-balanced) adjacency matrix. ... Weight-balanced and*doubly*stochastic*digraphs*are two classes of*digraphs*that play an essential role in a variety of coordination problems, including formation control, agreement, and distributed optimization ... In particular, we are indebted to a reviewer who suggested the formulation of the*doubly*stochastic weight assignment problem as a constrained maximum flow problem. ...##
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New constructions of Deza digraphs
[article]

2020
*
arXiv
*
pre-print

Deza

arXiv:2001.07281v2
fatcat:dq5ga3tsn5e3jmiqqkdsaaffga
*digraphs*were introduced in 2003 by Zhang and Wang as directed graph version of Deza graphs, that also generalize the notion of directed strongly*regular*graphs. ... In this paper we give several new constructions of Deza*digraphs*. Further, we introduce twin and Siamese twin (directed) Deza graphs and construct several examples. ... Divisible design*digraphs*(see [2] ) are natural generalization of*doubly**regular**asymmetric**digraphs*. ...##
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Distributed strategies for generating weight-balanced and doubly stochastic digraphs
[article]

2011
*
arXiv
*
pre-print

We refer to a

arXiv:0911.0232v6
fatcat:3ieah5x2njh67fi43lidff75yi
*digraph*as*doubly*stochasticable (weight-balanceable) if it admits a*doubly*stochastic (weight-balanced) adjacency matrix. ... Weight-balanced and*doubly*stochastic*digraphs*are two classes of*digraphs*that play an essential role in a variety of cooperative control problems, including formation control, distributed averaging, ... Then we refer to G = (V, E, A) as a C-*regular**digraph*. Necessary and sufficient conditions for*doubly*stochasticability. ...##
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Divisible design Cayley digraphs
[article]

2019
*
arXiv
*
pre-print

Divisible design

arXiv:1910.10991v1
fatcat:77vbrkirwjctnnt4rakso3psqm
*digraphs*which can be obtained as Cayley*digraphs*are studied. A characterization of divisible design Cayley*digraphs*in terms of the generating sets is given. ... Further, we give several constructions of divisible design Cayley*digraphs*and classify divisible design Cayley*digraphs*on v < 27 vertices. ... Divisible design*digraphs*are natural generalization of*doubly**regular**asymmetric*di-graphs. ...##
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Page 847 of Mathematical Reviews Vol. 47, Issue 4
[page]

1974
*
Mathematical Reviews
*

A a which eorems, simplex d num- fore at », Ont.)
4838
s in the 1-Kalb-
mono- 50, and ve that , Man.)
4839 ‘omatic

*regular*c index . exists ) paper red the COMBINATORICS existence of a*regular*graph of ... The authors use*doubly*stochastic matrices to obtain some elementary properties of directed graphs. ...##
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Algorithmic Approach to Non-symmetric 3-class Association Schemes
[chapter]

2009
*
Algorithmic Algebraic Combinatorics and Gröbner Bases
*

By Lemma 4, the directed graph is then a normally

doi:10.1007/978-3-642-01960-9_8
fatcat:jqnrrf5uxjhfnk3fno7lpid4ay
*regular**digraph*with µ = λ. Such*digraphs*are also known as*doubly**regular**asymmetric**digraphs*. ... Any*doubly**regular**asymmetric**digraph*with automorphism group of rank 4 is a relation of a non-symmetric association scheme with 3 classes. ...##
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Page 5935 of Mathematical Reviews Vol. , Issue 89K
[page]

1989
*
Mathematical Reviews
*

Toshimasa Watanabe (J-HROSE-A)
89k:05042 05C20
Ito, Noboru (J-PKNN-AM)

*Doubly**regular**asymmetric**digraphs*. Proceedings of the First Japan Conference on Graph Theory and Applications (Hakone, 1986). ... Obviously one can interpret such a design as an*asymmetric**digraph*. These objects have been studied in the case of a Hadamard design, in which case the*digraph*is a tournament [see ...
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