Toida's conjecture is true.

Dobson, Edward; Morris, Joy

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Displaying similar documents to “Toida's conjecture is true.”

Explicit Cayley covers of Kautz digraphs.

Brunat, Josep M. (2011)

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Automorphism groups of Cayley digraphs of $ℤ_{p}^{3}$ .

Dobson, Edward, Kovács, István (2009)

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Some non-normal Cayley digraphs of the generalized quaternion group of certain orders.

Dobson, Edward (2003)

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Automorphisms and enumeration of switching classes of tournaments.

Babai, L., Cameron, P.J. (2000)

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Frucht’s Theorem for the Digraph Factorial

Richard H. Hammack (2013)

Discussiones Mathematicae Graph Theory

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To every graph (or digraph) A, there is an associated automorphism group Aut(A). Frucht’s theorem asserts the converse association; that for any finite group G there is a graph (or digraph) A for which Aut(A) ∼= G. A new operation on digraphs was introduced recently as an aid in solving certain questions regarding cancellation over the direct product of digraphs. Given a digraph A, its factorial A! is certain digraph whose vertex set is the permutations of V (A). The arc set E(A!) forms...

A remark on almost Moore digraphs of degree three.

Baskoro, E.T., Miller, M., Širáň, J. (1997)

Acta Mathematica Universitatis Comenianae. New Series

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Automorphism groups of wreath product digraphs.

Dobson, Edward, Morris, Joy (2009)

The Electronic Journal of Combinatorics [electronic only]

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Some Results on 4-Transitive Digraphs

Patricio Ricardo García-Vázquez, César Hernández-Cruz (2017)

Discussiones Mathematicae Graph Theory

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Let D be a digraph with set of vertices V and set of arcs A. We say that D is k-transitive if for every pair of vertices u, v ∈ V, the existence of a uv-path of length k in D implies that (u, v) ∈ A. A 2-transitive digraph is a transitive digraph in the usual sense. A subset N of V is k-independent if for every pair of vertices u, v ∈ N, we have d(u, v), d(v, u) ≥ k; it is l-absorbent if for every u ∈ V N there exists v ∈ N such that d(u, v) ≤ l. A k-kernel of D is a k-independent and...

Underlying Graphs of 3-Quasi-Transitive Digraphs and 3-Transitive Digraphs

Ruixia Wang, Shiying Wang (2013)

Discussiones Mathematicae Graph Theory

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A digraph is 3-quasi-transitive (resp. 3-transitive), if for any path x0x1 x2x3 of length 3, x0 and x3 are adjacent (resp. x0 dominates x3). C´esar Hern´andez-Cruz conjectured that if D is a 3-quasi-transitive digraph, then the underlying graph of D, UG(D), admits a 3-transitive orientation. In this paper, we shall prove that the conjecture is true.

Reachability relations and the structure of transitive digraphs.

Seifter, Norbert, Trofimov, Vladimir I. (2009)

The Electronic Journal of Combinatorics [electronic only]

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4-Transitive Digraphs I: The Structure of Strong 4-Transitive Digraphs

César Hernández-Cruz (2013)

Discussiones Mathematicae Graph Theory

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Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A digraph D is transitive if for every three distinct vertices u, v,w ∈ V (D), (u, v), (v,w) ∈ A(D) implies that (u,w) ∈ A(D). This concept can be generalized as follows: A digraph is k-transitive if for every u, v ∈ V (D), the existence of a uv-directed path of length k in D implies that (u, v) ∈ A(D). A very useful structural characterization of transitive digraphs has been known for a...

On the proof of a theorem of Pálfy.

Dobson, Edward (2006)

The Electronic Journal of Combinatorics [electronic only]

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