The Spectrum of Tetrahedral Quadruple Systems

Wang, Jian; Liang, Miao; Du, Beiliang
July 2011
Graphs & Combinatorics;Jul2011, Vol. 27 Issue 4, p593
Academic Journal
n ordered analogue of quadruple systems is tetrahedral quadruple systems. A tetrahedral quadruple system of order v and index λ, TQS( v, λ), 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 called blocks, such that every directed 3-cycle on S is contained in exactly λ blocks of $${\mathcal{T}}$$ . When λ = 1, the spectrum problem of TQS( v, 1) has been completely determined. It is proved that a TQS( v, λ) exists if and only if λ( v − 1)( v − 2) ≡ 0 (mod 3), λ v( v − 1)( v − 2) ≡ 0 (mod 4) and v ≥ 4.


Related Articles

  • 3-TRANSITIVE DIGRAPHS. Hernández-Cruz, César // Discussiones Mathematicae: Graph Theory;2012, Vol. 32 Issue 3, p205 

    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) ∈ A(D). In this article strong 3-transitive digraphs are...

  • 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 = (Suδ), where Su is a graph G = (V,E), called the underlying graph of S and δ : E → {+,-} 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...

  • 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...

  • 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...

  • 4-TRANSITIVE DIGRAPHS I: THE STRUCTURE OF STRONG 4-TRANSITIVE DIGRAPHS. HERNÁNDEZ-CRUZ, CÉSAR // Discussiones Mathematicae: Graph Theory;2013, Vol. 33 Issue 2, p247 

    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...

  • On Sullivan's conjecture on cycles in 4-free and 5-free digraphs. Liang, Hao; Xu, Jun // Acta Mathematica Sinica;Jan2013, Vol. 29 Issue 1, p53 

    For a simple digraph G, let β( G) be the size of the smallest subset X ⊆ E( G) such that G−X has no directed cycles, and let γ( G) be the number of unordered pairs of nonadjacent vertices in G. A digraph G is called k-free if G has no directed cycles of length at most k. This...

  • 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...

  • 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 ≥ 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...


    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 ∈ N such that there is a monochromatic directed path from v to n....


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics