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The basis digraphs of p-schemes [article]

Ilia Ponomarenko, Amir Rahnamai Barghi
2007 arXiv   pre-print
It is proved that association 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.  ... 
arXiv:0710.0046v1 fatcat:od3yahsqa5ghngceqhtxuh537e

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

R A Freeman, T R Nelson, K M Lynch
2010 Proceedings of the 2010 American Control Conference  
We provide a set 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.  ... 
doi:10.1109/acc.2010.5530780 fatcat:arv5kvrwabcfhjmr4vuhaxhgme

Conflict-free channel set assignment for an optical cluster interconnection network based on rotator digraphs

Peng-Jun Wan
1998 Theoretical Computer Science  
In this paper, we propose 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.  ... 
doi:10.1016/s0304-3975(98)00064-4 fatcat:irmyn4wlr5hh3h45x7up4h72aq

On thin residues and basis digraphs of nilpotent table algebras and applications to nilpotent groups

Bangteng Xu
2012 Journal of Algebra  
In this paper we study characterizations 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.  ... 
doi:10.1016/j.jalgebra.2012.04.024 fatcat:uka5hostorc3dpzy6tk6e3tsu4

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.  ... 

Primitive weakly distance-regular circulant digraphs [article]

Akihiro Munemasa, Kaishun Wang, Yuefeng Yang
2019 arXiv   pre-print
We classify certain non-symmetric commutative association 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 ).  ... 
arXiv:1908.08658v1 fatcat:7epcwbihprdfrl7duzlazex2he

Sequencing with uncertain numerical data for makespan minimisation

T-C Lai, Y N Sotskov
1999 Journal of the Operational Research Society  
path relative to polytope T on 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;.  ... 
doi:10.1057/palgrave.jors.2600690 fatcat:pek6ulacs5h27oivqops2cujx4

Hoffman's coclique bound for normal regular digraphs, and nonsymmetric association schemes [article]

Hadi Kharaghani, Sho Suda
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.  ... 
arXiv:1511.07537v1 fatcat:hytvwrastvhtbhhqsxcxlyqcku

Weakly distance-regular digraphs

F. Comellas, M.A. Fiol, J. Gimbert, M. Mitjana
2004 Journal of combinatorial theory. Series B (Print)  
Some examples 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.  ... 
doi:10.1016/j.jctb.2003.07.003 fatcat:hgmu7ibtqfgavirlnic56iqk7u

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.  ... 

On the Spectrum of a Weakly Distance-Regular Digraph

F. Comellas, M.A. Fiol, J. Gimbert, M. Mitjana
2001 Electronic Notes in Discrete Mathematics  
Damerell adopted 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  ... 
doi:10.1016/s1571-0653(04)00364-6 fatcat:h2hd6lxwtjd5patxtfamz23dcu

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  ... 

Independent connections: an easy characterization of baseline-equivalent multistage interconnection networks

J.C. Bermond, J.M. Fourneau
1989 Theoretical Computer Science  
Finally, we show that if 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] .  ... 
doi:10.1016/0304-3975(89)90061-3 fatcat:35q5fwye7ja2jh472uqd457jey

Graph-Theoretic Approaches to Two-Sender Index Coding

Chandra Thapa, Lawrence Ong, Sarah J. Johnson
2016 2016 IEEE Globecom Workshops (GC Wkshps)  
Moreover, we extend 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.  ... 
doi:10.1109/glocomw.2016.7848917 dblp:conf/globecom/ThapaOJ16 fatcat:qzoxef6qynezbbld6i2uveq774
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