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The basis digraphs of p-schemes
[article]

2007
*
arXiv
*
pre-print

It is proved that association

arXiv:0710.0046v1
fatcat:od3yahsqa5ghngceqhtxuh537e
*schemes*with bipartite*basis*graphs are exactly 2-*schemes*. This result follows from a characterization*of**p*-*schemes*for an arbitrary prime*p*in terms*of**basis**digraphs*. ...*The**scheme*C is called regular, if G = R. Given R ∈ R **the**digraph*Γ(C, R) = (V R , R) is called*the**basis**digraph*(resp.*the**basis*graph)*of*a*scheme*C, if R ∈ R (resp. ... From [5,*p*.55] , it follows that*the**basis**digraph**of*a homogeneous*scheme*is strongly connected if and only if*the*corresponding*basis*graph is connected. ...##
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Page 242 of The Journal of the Operational Research Society Vol. 50, Issue 3
[page]

1999
*
The Journal of the Operational Research Society
*

path relative to polytope T on

*the**basis**of*Theorem 3. ... and without reducing all unnecessary paths on*the**basis**of*Theorem 3. ...##
###
A complete characterization of a class of robust linear average consensus protocols

2010
*
Proceedings of the 2010 American Control Conference
*

We provide a set

doi:10.1109/acc.2010.5530780
fatcat:arv5kvrwabcfhjmr4vuhaxhgme
*of*verifiable necessary and sufficient conditions for a member*of*a broad class*of*linear discretetime consensus protocols to guarantee*the*robust convergence*of**the*outputs*of**the*networked ... dynamics to*the*correct average consensus value. ...*The*characterization*of*nonlinear*schemes*, such as*the*consensus propagation*scheme**of*[8] , is a topic*of*future research. ...##
###
Conflict-free channel set assignment for an optical cluster interconnection network based on rotator digraphs

1998
*
Theoretical Computer Science
*

In this paper, we propose

doi:10.1016/s0304-3975(98)00064-4
fatcat:irmyn4wlr5hh3h45x7up4h72aq
*the*rotator*digraph*[5] as*the*cluster interconnection topology as it possesses many attractive properties. ... Each cluster employs a separate pair*of*broadcast and select couplers.*The*clusters are interconnected via fiber links according to a regular topology. ... This class*of*graphs uses a group-theoretic approach as a*basis*for defining*digraphs*. Let G be a finite group and S a set*of*generators for G. ...##
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On thin residues and basis digraphs of nilpotent table algebras and applications to nilpotent groups

2012
*
Journal of Algebra
*

In this paper we study characterizations

doi:10.1016/j.jalgebra.2012.04.024
fatcat:uka5hostorc3dpzy6tk6e3tsu4
*of*nilpotent table algebras in terms*of*thin residues; thin residue matrices; thin residue*digraphs*; and*basis**digraphs*. ... In particular, we give a conceptual explanation*of**the*results in Takegahara and Yoshida (2008) [TY]. ...*The*referee's valuable suggestions have improved*the*quality*of**the*paper. ...##
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Page 3517 of Mathematical Reviews Vol. , Issue 84i
[page]

1984
*
Mathematical Reviews
*

Kesel’man (Semiluki)
Harminc, Matus
On

*the*(m,n)-*basis**of*a*digraph*. (Russian summary) Math. Slovaca 30 (1980), no. 4, 401-404. Author’s review:*The*concept*of*an m-*basis*[see F. ... Using known results concerning solutions*of**digraphs**the*existence*of*an (m,n)-*basis*is proved: (i) for*digraphs*if n> 2m; (ii) for symmetric*digraphs*if n>m. ...##
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Primitive weakly distance-regular circulant digraphs
[article]

2019
*
arXiv
*
pre-print

We classify certain non-symmetric commutative association

arXiv:1908.08658v1
fatcat:7epcwbihprdfrl7duzlazex2he
*schemes*. As an application, we determine all*the*primitive weakly distance-regular circulant*digraphs*. ... In this paper, we show that*the*attached*schemes**of*primitive weakly distance-regular circulant*digraphs*satisfy*the*conditions*of*Theorem 1.1, and obtain*the*classification*of*such*digraphs*. ... For a prime power q =*p*m , q ≡ 3 (mod 4), let (GF(q), {R i } 2 i=0 ) denote*the*cyclotomic*scheme*Cyc(q, 2).*The*Paley*digraph**of*order q is defined as*the**digraph*(GF(q), R 1 ). ...##
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Sequencing with uncertain numerical data for makespan minimisation

1999
*
Journal of the Operational Research Society
*

path relative to polytope T on

doi:10.1057/palgrave.jors.2600690
fatcat:pek6ulacs5h27oivqops2cujx4
*the**basis**of*Theorem 3. ... For example, in*the*last iteration*of*General*Scheme**digraph*G, has to be compared with*the*set*of**digraphs*A(G)\ U‘z} C;. ...##
###
Hoffman's coclique bound for normal regular digraphs, and nonsymmetric association schemes
[article]

2015
*
arXiv
*
pre-print

*The*

*digraphs*provided here are relation graphs

*of*some nonsymmetric association

*schemes*. ... 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. ... A

*digraph*Γ = (X, E) is a relation graph

*of*an association

*scheme*with vertex set X if

*the*adjacency matrix

*of*Γ is one

*of*

*the*adjacency matrices

*of*

*the*association

*scheme*. ...

##
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Weakly distance-regular digraphs

2004
*
Journal of combinatorial theory. Series B (Print)
*

Some examples

doi:10.1016/j.jctb.2003.07.003
fatcat:hgmu7ibtqfgavirlnic56iqk7u
*of*these*digraphs*, such as*the*butterfly and*the*cycle prefix*digraph*which are interesting for their applications, are analyzed in*the*light*of**the*developed theory. ... We introduce*the*concept*of*weakly distance-regular*digraph*and study some*of*its basic properties. ... Acknowledgments*The*authors are indebted to*the*referees for helpful comments and suggestions which lead to numerous improvements*of**the*manuscript. ...##
###
Page 1734 of Mathematical Reviews Vol. , Issue 2004c
[page]

2004
*
Mathematical Reviews
*

., Aq) denote a complex character algebra with d > 2 which is

*P*-polynomial with respect to*the*ordering Ao, A),..., Ag*of**the*distinguished*basis*. ... We give some constructions*of*weakly distance-regular*digraphs*and discuss*the*connections to association*schemes*. ...##
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On the Spectrum of a Weakly Distance-Regular Digraph

2001
*
Electronic Notes in Discrete Mathematics
*

Damerell adopted

doi:10.1016/s1571-0653(04)00364-6
fatcat:h2hd6lxwtjd5patxtfamz23dcu
*the*strongest definition*of*distanceregularity, which is equivalent to say that*the*corresponding set*of*distance matrices {A i } D i=0 constitutes a commutative association*scheme*. ... We consider*the*class*of**digraphs*characterized by such a weaker condition, referred to as weakly distance-regular*digraphs*, and show that their spectrum can also be obtained from a smaller 'quotient*digraph*... Then,*the*representation*of*xp i in terms*of**the**basis*{*p*k } D k=0 must be*of**the*form xp i =*p*i x = min{i+1,D} k=0 γ k i*p*k (0 ≤ i ≤ D) where γ k i is*the*corresponding Fourier coefficient which must ...##
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Page 1710 of Mathematical Reviews Vol. , Issue 88d
[page]

1988
*
Mathematical Reviews
*

In this paper such
a collection is called a handle

*basis*. ... Then it is applied to*the*distance transitive graphs associated with*the*Hamming*schemes*to show that S,, wr Sz acting on*the*set*of*d-tuples from a set*of*size m is maximal as a unitransitive subgroup ...##
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Independent connections: an easy characterization of baseline-equivalent multistage interconnection networks

1989
*
Theoretical Computer Science
*

Finally, we show that if

doi:10.1016/0304-3975(89)90061-3
fatcat:35q5fwye7ja2jh472uqd457jey
*the*interconnection*scheme*is defined by using permutations on*the*links induced by a permutation*of**the*index digit (PIPID permutation) then*the*connection is independent. ... We define*the*interconnection*scheme*between two stages as a pair*of*functions (.1; g) which associate with a cell or node x, labelled as a binary string, his two sons f(x) and g(x). ... All*the*MI-*digraphs*with n stages satisfying*the*Banyan property*P*(*, n) and*P*(1, *) are isomorphic. For a proof see [12] . ...##
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Graph-Theoretic Approaches to Two-Sender Index Coding

2016
*
2016 IEEE Globecom Workshops (GC Wkshps)
*

Moreover, we extend

doi:10.1109/glocomw.2016.7848917
dblp:conf/globecom/ThapaOJ16
fatcat:qzoxef6qynezbbld6i2uveq774
*the*existing*schemes*for SSUIC, viz.,*the*cycle-cover*scheme*,*the*clique-cover*scheme*, and*the*local-chromatic*scheme*to*the*corresponding*schemes*for TSUIC. ...*The*index coding in this setup is called two-sender unicast index coding (TSUIC).*The*main aim*of*TSUIC is to minimize*the*total number*of*transmissions required by*the*two senders. ... In*the*example,*p*(D, G o ) is strictly less than α. Note that this way*of*partitioning is not possible with*the*trivial extension*of**the*local-chromatic*scheme*stated in Proposition 2. ...
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