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A class of vertex-transitive digraphs, II

1982
*
Journal of combinatorial theory. Series B (Print)
*

We also determine the number

doi:10.1016/0095-8956(82)90009-0
fatcat:amji77nrxzaelndspixbe7l6p4
*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... ...##
###
Super-connected arc-transitive digraphs

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. ...

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

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 ...

##
###
Bounded bitolerance digraphs

2000
*
Discrete Mathematics
*

In this paper, we introduce directed versions

doi:10.1016/s0012-365x(99)00220-4
fatcat:ckboonabdzd63d5o3cmtvlvwru
*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. ...##
###
On Characterizations for Subclasses of Directed Co-Graphs
[article]

2020
*
arXiv
*
pre-print

There are only

arXiv:1907.00801v2
fatcat:2d755okkgbfyhet6rki4adqw74
*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. ...##
###
On labeled vertex-transitive digraphs with a prime number of vertices

1983
*
Discrete Mathematics
*

We enumerate, up to isomorphism, several

doi:10.1016/0012-365x(83)90126-7
fatcat:zoouutbo6za4joie2qb2vtxuqq
*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! ...##
###
Distance transitive digraphs

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. ...

##
###
Some general aspects of the framing number of a digraph

1998
*
Discrete Applied Mathematics
*

, + k'l. and the lexicographic product

doi:10.1016/s0166-218x(97)00127-3
fatcat:g3tmx2nurzfozfwhvn5ffcbaaq
*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*. ...##
###
Classes of Digraphs
[chapter]

2009
*
Springer Monographs in Mathematics
*

These

doi:10.1007/978-1-84800-998-1_2
fatcat:7p2twq5kanaovbwcwmylqwihmi
*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*. ...##
###
Characterization of (m, 1)-transitive and (3,2)-transitive semi-complete directed graphs

1994
*
Discrete Mathematics
*

We describe the structure

doi:10.1016/0012-365x(94)00060-v
fatcat:aalzrhxp6vc5tn6knwd3cmqsaq
*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. ...##
###
Solving the kernel perfect problem by (simple) forbidden subdigraphs for digraphs in some families of generalized tournaments and generalized bipartite tournaments
[article]

2018
*
arXiv
*
pre-print

asymmetric 3-anti-quasi-

arXiv:1712.00138v4
fatcat:o7ezxb5tizf2dhcwkb4srdmoau
*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*. ...##
###
Green's Symmetries in Finite Digraphs

2011
*
Symmetry
*

The semigroup D V

doi:10.3390/sym3030564
fatcat:i7324yqxdbcmrncxe6oltem4tu
*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. ...##
###
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

2010
*
Journal of combinatorial theory. Series B (Print)
*

We discuss

doi:10.1016/j.jctb.2010.03.002
fatcat:hxx3hv2kjfcobj3c7f2uk5kvci
*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 ...##
###
The Separated Box Product of Two Digraphs
[article]

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. ...

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