TITLE

# 3-TRANSITIVE DIGRAPHS

AUTHOR(S)
Hernández-Cruz, César
PUB. DATE
July 2012
SOURCE
Discussiones Mathematicae: Graph Theory;2012, Vol. 32 Issue 3, p205
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
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 3-transitive if the existence of the directed path (u; v;w; x) of length 3 in D implies the existence of the arc (u, x) âˆˆ A(D). In this article strong 3-transitive digraphs are characterized and the structure of non-strong 3-transitive digraphs is described. The results are used, e.g., to characterize 3-transitive digraphs that are transitive and to characterize 3-transitive digraphs with a kernel.
ACCESSION #
74732879

## Related Articles

• ON MONOCHROMATIC PATHS AND BICOLORED SUBDIGRAPHS IN ARC-COLORED TOURNAMENTS. DELGADO-ESCALANTE, PIETRA; GALEANA-SANCHEZ, HORTENSIA // Discussiones Mathematicae: Graph Theory;2011, Vol. 31 Issue 4, p791

Consider an arc-colored digraph. A set of vertices N is a kernel by monochromatic paths if all pairs of distinct vertices of N have no monochromatic directed path between them and if for every vertex v not in N there exists n âˆˆ N such that there is a monochromatic directed path from v to n....

• SOME RESULTS ON SEMI-TOTAL SIGNED GRAPHS. SINHA, DEEPA; GARG, PRAVIN // Discussiones Mathematicae: Graph Theory;2011, Vol. 31 Issue 4, p625

A signed graph (or sigraph in short) is an ordered pair S = (SuÎ´), where Su is a graph G = (V,E), called the underlying graph of S and Î´ : E â†’ {+,-} is a function from the edge set E of Suinto the set {+,-}, called the signature of S. The x-line sigraph of S denoted by L x (S) is a...

• Majority Domatic Number - I. Manora, J. Joseline; Swaminathan, V. // Global Journal of Pure & Applied Mathematics;2010, Vol. 6 Issue 3, p275

In any democratic set up, the party which has majority of seats is given the opportunity to rule the state. To model such instances, the concept majority domination is introduced. This chapter deals with partitioning the vertex set into as many disjoint subsets, each being a majority dominating...

• THE i-CHORDS OF CYCLES AND PATHS. MCKEE, TERRY A. // Discussiones Mathematicae: Graph Theory;2012, Vol. 32 Issue 4, p607

An i-chord of a cycle or path is an edge whose endpoints are a distance i â‰¥ 2 apart along the cycle or path. Motivated by many standard graph classes being describable by the existence of chords, we investigate what happens when i-chords are required for specific values of i. Results...

• Graph Equation for Line Graphs and m-Step Graphs. Kim, Seog-Jin; Kim, Suh-Ryung; Lee, Jung; Park, Won; Sano, Yoshio // Graphs & Combinatorics;Nov2012, Vol. 28 Issue 6, p831

Given a graph G, the m-step graph of G, denoted by S( G), has the same vertex set as G and an edge between two distinct vertices u and v if there is a walk of length m from u to v. The line graph of G, denoted by L( G), is a graph such that the vertex set of L( G) is the edge set of G and two...

• An Algorithm to Detect Cycle in an Undirected Graph. Kumar, Anand; Jani, N. N. // International Journal of Computational Intelligence Research;2010, Vol. 6 Issue 2, p305

This paper presents a novel algorithm to detect cycles in a graph. The graph may be of any type. Cycles are available in a graph and in much real life application; it is required to know the existence of cycles in a graph. This algorithm is developed in the context of network design problem but...

• The Spectrum of Tetrahedral Quadruple Systems. Wang, Jian; Liang, Miao; Du, Beiliang // Graphs & Combinatorics;Jul2011, Vol. 27 Issue 4, p593

n ordered analogue of quadruple systems is tetrahedral quadruple systems. A tetrahedral quadruple system of order v and index Î», TQS( v, Î»), is a pair $${(S, \mathcal{T})}$$ where S is a finite set of v elements and $${\mathcal{T}}$$ is a family of oriented tetrahedrons of elements of S...

• FINITE TOPOLOGIES AND DIGRAPHS. MARIJUÁN, CARLOS // Proyecciones - Journal of Mathematics;2010, Vol. 29 Issue 3, p291

In this paper we study the relation between finite topologies and digraphs. We associate a digraph to a topology by means of the "specialization" relation between points in the topology. Reciprocally, we associate a topology to each digraph, taking the sets of vertices adjacent (in the digraph)...

• TREES WITH EQUAL 2-DOMINATION AND 2-INDEPENDENCE NUMBERS. Chellali, Mustapha; Meddah, Nacéra // Discussiones Mathematicae: Graph Theory;2012, Vol. 32 Issue 3, p263

Let G = (V,E) be a graph. A subset S of V is a 2-dominating set if every vertex of V - S is dominated at least 2 times, and S is a 2-independent set of G if every vertex of S has at most one neighbor in S. The minimum cardinality of a 2-dominating set a of G is the 2-domination number Î³2(G)...

Share