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The spectra of subKautz and cyclic Kautz digraphs

C. Dalfó
2017 Linear Algebra and its Applications  
In this paper we propose a new method to obtain the complete spectra of subKautz sK(d, 2) and cyclic Kautz CK(d, 3) digraphs, for all d ≥ 3, through the Hoffman-McAndrew polynomial and regular partitions  ...  Closely related with these, the cyclic Kautz CK(d, ) and the subKautz sK(d, 2) digraphs were recently introduced by Böhmová, Huemer and the author.  ...  This research has also received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No 734922.  ... 
doi:10.1016/j.laa.2017.05.046 fatcat:pnzrtkcjanavzhojotng77vcc4

The diameter of cyclic Kautz digraphs

Katerina Böhmová, Cristina Dalfó, Clemens Huemer
2017 Filomat  
Moreover, we construct the modified cyclic Kautz digraphs MCK(d, ) to obtain the same diameter as in the Kautz digraphs, and we show that MCK(d, ) are d-out-regular.  ...  The cyclic Kautz digraphs CK(d, ) have arcs between vertices a 1 a 2 . . . a and a 2 . . . a a +1 , with a 1 = a , a 2 = a +1 , and a i = a i+1 for i = 1, . . . , − 1.  ...  Theorem 3. 1 1 The modified cyclic Kautz digraph MCK(d, ) has the following properties:(a) It is d-out-regular.  ... 
doi:10.2298/fil1720551b fatcat:foxmp3fmhjdkrei4p3323m4tce

Eulerian iterated line graphs and digraphs

Erich Prisner
2001 Discrete Mathematics  
It is shown that every strongly connected digraph has either at most one or inÿnitely many of its iterated line digraphs eulerian.  ...  The proof uses a canonical way of 'wrapping' a digraph D around a directed cycle whose length is the greatest common divisor of all directed-cycle lengths of D.  ...  Acknowledgements This work was supported by the Deutsche Forschungsgemeinschaft under Grant No.  ... 
doi:10.1016/s0012-365x(00)00450-7 fatcat:xw4tvihj7rg5vlg77mw5mmxwdi

Cayley graphs of more than one abelian group

Edward Dobson, Joy Morris
2021 The Art of Discrete and Applied Mathematics  
or not a natural subgroup of the full automorphism group contains more than one regular abelian group up to isomorphism (as opposed to the full automorphism group).  ...  We show that for certain integers n, the problem of whether or not a Cayley digraph Γ of Z n is also isomorphic to a Cayley digraph of some other abelian group G of order n reduces to the question of whether  ...  The conjugacy of regular cyclic subgroups is also noted in Corollary 2 of [15] , but the fact that all regular abelian subgroups are cyclic is proved in the Li paper.  ... 
doi:10.26493/2590-9770.1352.4dc fatcat:u2yogslvljgp5keg5cz63hmmfe

Page 652 of Mathematical Reviews Vol. , Issue 91B [page]

1991 Mathematical Reviews  
Manvel and Osborne [“Walks in covering spaces”, in Proceedings of the Sixth International Conference on the Theory of Graphs, to appear] proved that a homomorphism between connected regular digraphs has  ...  orbits, then A is equivalent to the cyclic incidence matrix of the cyclic difference set in GF(p), where v = p = 4x?  ... 

Isomorphic factorization of de Bruijn digraphs

Yukio Shibata, Toru Hasunuma, Sanae Fukuda
2000 Discrete Mathematics  
In this paper, we present several relations among the Kronecker product, the line digraph operation, and isomorphic factorization.  ...  Then, we generalize this result to extended de Bruijn digraphs (the Kronecker product of de Bruijn digraphs).  ...  Acknowledgements We are grateful to the referees for their invaluable comments and suggestions that improved the paper.  ... 
doi:10.1016/s0012-365x(99)00304-0 fatcat:ww7geqq4rjbcllpp25hgulquqm

From Subkautz Digraphs to Cyclic Kautz Digraphs

C. DALFÓ
2018 Journal of Interconnection Networks (JOIN)  
In this paper we propose a new approach to cyclic Kautz digraphs by introducing the family of subKautz digraphs sK(d, ), from where the cyclic Kautz digraphs can be obtained as line digraphs.  ...  Closely related with these, the cyclic Kautz digraphs CK(d, ) were recently introduced by Böhmová, Huemer and the author, and some of its distance-related parameters were fixed.  ...  Observe that, since CK(d, 3) is the line digraph of sK(d, 2), the respective mean distance satisfies the inequality δ < δ * , in concordance with the results by Fiol, Yebra, and Alegre [7] .  ... 
doi:10.1142/s0219265918500068 fatcat:fcbszgxcxbeehp3xob43yb36ra

Cayley graphs of more than one abelian group [article]

Edward Dobson, Joy Morris
2020 arXiv   pre-print
or not a natural subgroup of the full automorphism group contains more than one regular abelian group up to isomorphism (as opposed to the full automorphism group).  ...  We show that for certain integers n, the problem of whether or not a Cayley digraph Γ of ℤ_n is also isomorphic to a Cayley digraph of some other abelian group G of order n reduces to the question of whether  ...  The conjugacy of regular cyclic subgroups is also noted in Corollary 2 of [15] , but the fact that all regular abelian subgroups are cyclic is proved in the Li paper.  ... 
arXiv:1505.05771v2 fatcat:5et7o2qdjfakxa6znheef3tnoq

TRANSMISSION FAULT-TOLERANCE OF ITERATED LINE DIGRAPHS

LU RUAN, SHITOU HAN, DEYING LI, HUNG Q. NGO, SCOTT C.-H. HUANG
2004 Journal of Interconnection Networks (JOIN)  
In this paper, we will establish a general result on super line-connectivity based on the line digraph iteration which improves and generalizes several existing results in the literature.  ...  Many interconnection networks can be constructed with line digraph iterations.  ...  Let d 2. Suppose G is a d-regular digraph that each vertex has at most one loop.  ... 
doi:10.1142/s021926590400126x fatcat:bbn6pnbzsbexpa6tjz4mxwmc7i

Permutation Groups with a Cyclic Regular Subgroup and Arc Transitive Circulants

Cai Heng Li
2005 Journal of Algebraic Combinatorics  
, that is, Aut has a normal cyclic regular subgroup.  ...  A description is given of finite permutation groups containing a cyclic regular subgroup.  ...  The author is very grateful to one referee for his constructive suggestions, and especially for his formulating Theorem 2.3, which leads to the very short proof for Theorem 1.2 presented in this paper.  ... 
doi:10.1007/s10801-005-6903-3 fatcat:neqjcxaninhmrbnxbdpdjpx3hu

An algebraic approach to lifts of digraphs

C. Dalfó, M.A. Fiol, M. Miller, J. Ryan, J. Širáň
2019 Discrete Applied Mathematics  
As some examples of our techniques, we study some basic properties of the Alegre digraph.  ...  We study the relationship between two key concepts in the theory of (di)graphs: the quotient digraph, and the lift Γ α of a base (voltage) digraph.  ...  In Section 2 we present the basic definition and results on regular partitions and their corresponding quotient digraphs. In Section 3, we recall the definitions of voltage and lifted digraphs.  ... 
doi:10.1016/j.dam.2018.10.040 fatcat:5twhh4psmran7ccy3pth6wheui

An algebraic approach to lifts of digraphs [article]

C. Dalfó, M.A. Fiol, M. Miller, J. Ryan, J. Širáň
2017 arXiv   pre-print
As some examples of our techniques, we study some basic properties of the Alegre digraph.  ...  We study the relationship between two key concepts in the theory of (di)graphs: the quotient digraph, and the lift Γ^α of a base (voltage) digraph.  ...  In Section 2 we present the basic definition and results on regular partitions and their corresponding quotient digraphs. In Section 3, we recall the definitions of voltage and lifted digraphs.  ... 
arXiv:1612.08855v2 fatcat:gfw225mt75dfxdn35vsbh64lqe

Page 778 of Mathematical Reviews Vol. , Issue 2001B [page]

2001 Mathematical Reviews  
In this paper we determine the completeness of some decomposable properties and we characterize the decomposable properties of completeness 2.”  ...  Summary: “This note is a survey on 1-factorizations of mini- mally r-regular bigraphs, i.e. graphs in which every |-factor lies in precisely one |-factorization.”  ... 

On Cyclic Kautz Digraphs [article]

Katerina Böhmová, Cristina Dalfó, Clemens Huemer
2015 arXiv   pre-print
Moreover, we construct the modified cyclic Kautz digraphs MCK(d,ℓ) to obtain the same diameter as in the Kautz digraphs, and we show that MCK(d,ℓ) are d-out-regular.  ...  This new family is called modified cyclic digraphs MCK(d,ℓ) and it is derived from the Kautz digraphs K(d,ℓ). non-regular digraphs with minimal diameter given their number of vertices and out-degree.  ...  Digraph G is called d-out-regular if δ + G (v) = d for all v ∈ V , d-in-regular if δ − G (v) = d for all v ∈ V , and d-regular if δ + G (v) = δ − G (v) = d for all v ∈ V . 2 Parameters of the cyclic Kautz  ... 
arXiv:1512.05917v1 fatcat:yen3e24yajeevnzr65z55sjl4a

The Diameter of Cyclic Kautz Digraphs

K. Böhmová, C. Dalfó, C. Huemer
2015 Electronic Notes in Discrete Mathematics  
consecutive characters in the sequence are different (as in Kautz digraphs), and now also requiring that a1 = a .  ...  We present a new kind of digraphs, called cyclic Kautz digraphs CK(d, ), which are subdigraphs of the well-known Kautz digraphs K(d, ).  ...  We want to thank the anonymous referees for their reviews, which significantly contributed to improve the quality of this publication.  ... 
doi:10.1016/j.endm.2015.06.044 fatcat:cnh6psssffglxlele3fiklpmmi
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