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A class of vertex-transitive digraphs, II

Chong-Yun Chao, Jacqueline G Wells
1982 Journal of combinatorial theory. Series B (Print)  
We also determine the number of non-isomorphic classes of self-complementary, vertex-transitive digraphs with a prime number p vertices, and the number of selfcomplementary strongly vertex-transitive digraphs  ...  The nonisomorphic classes of strongly vertex-transitive digraphs with p vertices are also enumerated.  ...  The non-isomorphic classes of vertex-transitive digraphs with a prime number p vertices whose group of automorphisms ?(S, zq>, where S=(Ol...  ... 
doi:10.1016/0095-8956(82)90009-0 fatcat:amji77nrxzaelndspixbe7l6p4

Super-connected arc-transitive digraphs

Jixiang Meng, Zhao Zhang
2009 Discrete Applied Mathematics  
A digraph is said to be super-connected if every minimum vertex cut is the out-neighbor set or in-neighbor set of a vertex.  ...  In this paper, we prove that a strongly connected arc-transitive oriented graph is either reducible or super-connected.  ...  Acknowledgements We would like to appreciate the anonymous referees for the valuable suggestions which help us a lot in refining the presentation of this paper.  ... 
doi:10.1016/j.dam.2008.08.018 fatcat:szqnicoekre3tdq6yohagvpevm

Infinite arc-transitive and highly-arc-transitive digraphs [article]

Rögnvaldur G. Möller, Norbert Seifter University of Ljubljana, Ljubljana, Slovenia
2018 arXiv   pre-print
A detailed description of the structure of two-ended arc-transitive digraphs is given.  ...  These are then applied to give a complete classification of two-ended highly-arc-transitive digraphs with prime in- and out-valencies.  ...  When σ is an equivalence relation on the vertex set of a digraph Γ we can form the quotient digraph Γ/σ which has the set of σ-classes as a vertex set and if A and B are two σ-classes then (A, B) is an  ... 
arXiv:1811.02995v2 fatcat:djzj3pforfdvlonkcxfxt65t2m

Bounded bitolerance digraphs

Kenneth P. Bogart, Ann N. Trenk
2000 Discrete Mathematics  
In this paper, we introduce directed versions of the classes of tolerance graphs. We characterize the class of bounded bitolerance digraphs in terms of interval orders.  ...  Math. 9 (1984) 157-170) as a generalization of interval graphs. Several variations of bounded tolerance graphs have been studied, including bounded bitolerance graphs.  ...  Acknowledgements The authors would like to thank one of the referees for detailed suggestions that greatly improved this paper.  ... 
doi:10.1016/s0012-365x(99)00220-4 fatcat:ckboonabdzd63d5o3cmtvlvwru

On Characterizations for Subclasses of Directed Co-Graphs [article]

Frank Gurski, Dominique Komander, Carolin Rehs
2020 arXiv   pre-print
There are only a few versions of subclasses of directed co-graphs until now.  ...  Directed co-graphs are precisely those digraphs which can be defined from the single vertex graph by applying the disjoint union, order composition, and series composition.  ...  By G 1 and G 2 we denote graphs of the class X, by I we denote an edgeless graph, by K we denote a bidirectional complete digraph, and by T we denote a transitive tournament.  ... 
arXiv:1907.00801v2 fatcat:2d755okkgbfyhet6rki4adqw74

On labeled vertex-transitive digraphs with a prime number of vertices

Chong-Yun Chao, Jacqueline G. Wells
1983 Discrete Mathematics  
We enumerate, up to isomorphism, several classes of labeled vertex-transitive digraphs with a prime number of vertices. There are many unsolvedi enumeration problems stated in [S].  ...  Here, we give some partial answer to the problems posed on p. 181 in [S], i.e., bj using some of the results in [3] and [4], we enumerate several classes of labeled vertex-transitive digraphs with a prime  ...  In [3] , Theorem 3 states that the grcnp of automorphisms r(X) of a non-null and non-complete vertex-transitive di!  ... 
doi:10.1016/0012-365x(83)90126-7 fatcat:zoouutbo6za4joie2qb2vtxuqq

Distance transitive digraphs

Clement W.H. Lam
1980 Discrete Mathematics  
A digraph is said to be distance-transitive if for all vertices u, v, x, y such that d(u, v) = d(x, y) there is an automorphism w of the digraph such that T(U) = x and T(V) = y.  ...  Section 4 proves that every distance-transitive digraph with diameter 2 is a balanced incomplete block design with the Hadamard parameters.  ...  Acknowkdgewents The author would like to thank the referees for their critical comments, suggestion fot improvement and proofs of some results. The author would also like to thank H.H.  ... 
doi:10.1016/0012-365x(80)90155-7 fatcat:rwhs33ulwnh4xehflykx6tlyem

Some general aspects of the framing number of a digraph

Michael A. Henning, Hiren Maharaj
1998 Discrete Applied Mathematics  
, + k'l. and the lexicographic product of a transitive tournament and a vertex transitive digraph.  ...  The framing number is determined for a number of classes of digraphs, including a class of digraphs whose underlying graph is a complete bipartite graph, a class of digraphs whose underlying graph is C  ...  of digraphs.  ... 
doi:10.1016/s0166-218x(97)00127-3 fatcat:g3tmx2nurzfozfwhvn5ffcbaaq

Classes of Digraphs [chapter]

Jørgen Bang-Jensen, Gregory Z. Gutin
2009 Springer Monographs in Mathematics  
These digraphs are studied in many other sections of our book. In Section 2.3, we introduce and study the transitive closure and a transitive reduction of a digraph.  ...  An interesting generalization of transitive digraphs, the class of quasitransitive digraphs, is considered in Section 2.7.  ...  By the definition of a transitive digraph, a 2-cycle xyx does not force a loop at x and y. . Classes of Digraphs . Classes of Digraphs . Classes of Digraphs .  ... 
doi:10.1007/978-1-84800-998-1_2 fatcat:7p2twq5kanaovbwcwmylqwihmi

Characterization of (m, 1)-transitive and (3,2)-transitive semi-complete directed graphs

Zsolt Tuza
1994 Discrete Mathematics  
We describe the structure of those (m, 1)-transitive and (3,2)-transitive directed graphs in which each pair of vertices is adjacent by an arc in at least one direction, and present an algorithm with running  ...  A directed graph is called (m, k)-transitive if for every directed path x0x1 . ..x. there is a directed path y,y, . ..yt such that x0 =y ", x,=yl" and {yiIO<iik}c{xiIO<i<m}.  ...  and to the referees for their helpful comments on an earlier version of the paper.  ... 
doi:10.1016/0012-365x(94)00060-v fatcat:aalzrhxp6vc5tn6knwd3cmqsaq

Solving the kernel perfect problem by (simple) forbidden subdigraphs for digraphs in some families of generalized tournaments and generalized bipartite tournaments [article]

H. Galeana-Sánchez, M. Olsen
2018 arXiv   pre-print
asymmetric 3-anti-quasi-transitive TT_3-free and we state that the problem of determining whether a digraph of one of these families is CKI is polynomial, giving a solution to a problem closely related  ...  In this paper we characterize the CKI- and KP-digraphs for the following families of digraphs: locally in-/out-semicomplete, asymmetric arc-locally in-/out-semicomplete, asymmetric 3-quasi-transitive and  ...  locally out-semicomplete) is a quite wider class than the class of locally semicomplete digraphs.  ... 
arXiv:1712.00138v4 fatcat:o7ezxb5tizf2dhcwkb4srdmoau

Green's Symmetries in Finite Digraphs

Allen D. Parks
2011 Symmetry  
The semigroup D V of digraphs on a set V of n labeled vertices is defined.  ...  transform one digraph into another within the same equivalence class, i.e., these digraphs exhibit Green's isoneighborhood symmetries; and (ii) D equivalent digraphs are characterized by isomorphic inclusion  ...  Acknowledgements This work was supported by a grant from the Naval Surface Warfare Center Dahlgren Division's In-house Laboratory Independent Research Program sponsored by the Office of Naval Research.  ... 
doi:10.3390/sym3030564 fatcat:i7324yqxdbcmrncxe6oltem4tu

Page 3280 of Mathematical Reviews Vol. , Issue 85h [page]

1985 Mathematical Reviews  
In the first paper the author extends the notion of a circulant to a class of graphs called multi- dimensional circulants, consisting of all vertex transitive graphs with an automorphism group containing  ...  Various properties of these graphs are studied in relation to the problem of characterizing graph-theoretically the class of vertex transitive graphs. This has been a topic of recent interest.  ... 

On the vertex-stabiliser in arc-transitive digraphs

Primož Potočnik, Gabriel Verret
2010 Journal of combinatorial theory. Series B (Print)  
We discuss a possible approach to the study of finite arc-transitive digraphs and prove an upper bound on the order of a vertexstabiliser in locally cyclic arc-transitive digraphs of prime outvalence.  ...  Acknowledgment The authors acknowledge the financial support of the Slovenian Research Agency ARRS, grant No. J1-0540.  ...  To show that the mapping from the statement of (ii) is well defined and bijective, observe that, in Pl( Γ ), the equivalence class A 1 (u, v) of a vertex (u, v) of Pl( Γ ) consists of all the arcs of Γ  ... 
doi:10.1016/j.jctb.2010.03.002 fatcat:hxx3hv2kjfcobj3c7f2uk5kvci

The Separated Box Product of Two Digraphs [article]

Primož Potočnik, Stephen Wilson
2015 arXiv   pre-print
A new product construction of graphs and digraphs, based on the standard box product of graphs and called the separated box product, is presented, and several of its properties are discussed.  ...  An application of this construction to the case of tetravalent edge-transitive graphs is discussed in detail.  ...  Label the alterclasses of Γ 1 and Γ 2 by Z s and Z t in such a way that a and x are in the classes labelled 0 and every dart with its initial vertex in class i has its terminal vertex in class i + 1.  ... 
arXiv:1511.00623v1 fatcat:vels32zxtvgg3ajjwdivngsfh4
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