Nonderogatory unicyclic digraphs.
Bravo, Diego, Rada, Juan (2007)
International Journal of Mathematics and Mathematical Sciences
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Bravo, Diego, Rada, Juan (2007)
International Journal of Mathematics and Mathematical Sciences
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Susan van Aardt, Marietjie Frick, Joy Singleton (2013)
Discussiones Mathematicae Graph Theory
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In 1982 Laborde, Payan and Xuong [Independent sets and longest directed paths in digraphs, in: Graphs and other combinatorial topics (Prague, 1982) 173-177 (Teubner-Texte Math., 59 1983)] conjectured that every digraph has an independent detour transversal (IDT), i.e. an independent set which intersects every longest path. Havet [Stable set meeting every longest path, Discrete Math. 289 (2004) 169-173] showed that the conjecture holds for digraphs with independence number two. A digraph...
César Hernández-Cruz, Juan José Montellano-Ballesteros (2014)
Discussiones Mathematicae Graph Theory
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A digraph D is k-transitive if the existence of a directed path (v0, v1, . . . , vk), of length k implies that (v0, vk) ∈ A(D). Clearly, a 2-transitive digraph is a transitive digraph in the usual sense. Transitive digraphs have been characterized as compositions of complete digraphs on an acyclic transitive digraph. Also, strong 3 and 4-transitive digraphs have been characterized. In this work we analyze the structure of strong k-transitive digraphs having a cycle of length at least...
Bohdan Zelinka (2005)
Czechoslovak Mathematical Journal
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The concept of signed domination number of an undirected graph (introduced by J. E. Dunbar, S. T. Hedetniemi, M. A. Henning and P. J. Slater) is transferred to directed graphs. Exact values are found for particular types of tournaments. It is proved that for digraphs with a directed Hamiltonian cycle the signed domination number may be arbitrarily small.
Gary Chartrand, Don R. Lick (1971)
Czechoslovak Mathematical Journal
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Poet, Jeffrey, Shader, Bryan L. (1998)
The Electronic Journal of Combinatorics [electronic only]
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Davide C. Demaria, José Carlos de Souza Kiihl (1991)
Publicacions Matemàtiques
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Homotopic methods are employed for the characterization of the complete digraphs which are the composition of non-trivial highly regular tournaments.
Lim, Chjan C., Van Patten, Gregory K. (2001)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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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...
Arthur H. Busch, Michael S. Jacobson, K. Brooks Reid (2005)
Discussiones Mathematicae Graph Theory
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A digraph D = (V,A) is arc-traceable if for each arc xy in A, xy lies on a directed path containing all the vertices of V, i.e., hamiltonian path. We prove a conjecture of Quintas [7]: if D is arc-traceable, then the condensation of D is a directed path. We show that the converse of this conjecture is false by providing an example of an upset tournament which is not arc-traceable. We then give a characterization for upset tournaments in terms of their score sequences, characterize which...