# The Spectrum of Tetrahedral Quadruple Systems

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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 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...

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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...

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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...

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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 âˆˆ V (D), (u, v), (v, w) âˆˆ A(D) implies that (u, w) âˆˆ A(D). This concept can be generalized as follows: A digraph...

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For a simple digraph G, let Î²( G) be the size of the smallest subset X âŠ† E( G) such that Gâˆ’X has no directed cycles, and let Î³( 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 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...

- 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....