Given a digraph D, its competition graph has the same vertex set and an edge between two vertices x and y if there is a vertex u so that (x, u) and (y, u) are arcs of D. Motivated by a problem of communications, we study the competition graphs of the special digraphs known as semiorders. This leads us to define a conditions on digraphs called C(p) and C(p) and to study the graphs arising as com...

We consider vertex coloring of an acyclic digraph ~ G in such a way that two vertices which have a common ancestor in ~ G receive distinct colors. Such colorings arise in a natural way when bounding space for various genetic data for efficient analysis. We discuss the corresponding down-chromatic number and derive an upper bound as a function of D(~ G), the maximum number of descendants of a gi...

An inductive inference algorithm for inferring cyclic interleaving expressions from homing sequences is presented. The restricted language studied uses a synchronized interleaving or shuue operator, which is an important component in algebraic theories of concurrency. Expressions of this language denote concurrent perpetual processes that communicate via synchronized handshaking. The paper intr...

Jirasek, J., Some remarks on Adam’s conjecture for simple directed graphs, Discrete Mathematics 108 (1992) 327-332. The classes of multidigraphs for which Adam’s conjecture (that any digraph containing a directed cycle has an arc whose reversal decreases the total number of directed cycles) does not hold, were described in Grinberg (1988), Jirasek (1987) and Thomassen (1987). The question remai...

We consider vertex coloring of an acyclic digraph ~ G in such a way that two vertices which have a common ancestor in ~ G receive distinct colors. Such colorings arise in a natural way when bounding space for various genetic data for efficient analysis. We discuss the corresponding down-chromatic number and derive an upper bound as a function of D(~ G), the maximum number of descendants of a gi...

A subset of vertices of a graph G is called a feedback vertex set of G if its removal results in an acyclic subgraph. Let f (d, n) denote the minimum cardinality over all feedback vertex sets of the de Bruijn digraph B(d, n). This paper proves that for any integers d ≥ 2 and n ≥ 2 f (d, n) =  1 n ∑ i|n diφ (n i ) for 2 ≤ n ≤ 4; dn n + O(ndn−4) for n ≥ 5, where i | nmeans i divides n, and ...

Let D be a digraph with vertex set V(D) .For vertex v V(D), the degree of v, denoted by d(v), is defined as the minimum value if its out-degree  and its in-degree . Now let D be a digraph with minimum degree  and edge-connectivity If  is real number, then the zeroth-order general Randic index is defined by   .  A digraph is maximally edge-connected if . In this paper we present sufficient condi...

For a local tournament D with minimum out-degree δ, minimum indegree δ− and irregularity ig(D), we give a lower bound on the connectivity of D, namely κ(D) ≥ (2 ·max{δ+, δ−}+ 1− ig(D))/3 if there exists a minimum separating set S such that D − S i is a tournament, and κ(D) ≥ (2 ·max{δ+, δ−}+ 2|δ+ − δ−|+ 1− 2ig(D))/3 otherwise. This generalizes a result on tournaments presented by C. Thomassen [...

Since group consensus (GC) control accounts for one-half of the multi-robot coordination domain, as does complete control, this paper will formulate a certain kind GC and bipartite (GBC) in finite time multi-agent systems (MAS). It should be noted that key to work is information transfer under acyclic partition networks zero-sum between groups cooperative–competitive interaction. The general fi...

A polytopal digraph G(P ) is an orientation of the skeleton of a convex polytope P . The possible non-degenerate pivot operations of the simplex method in solving a linear program over P can be represented as a special polytopal digraph known as an LP digraph. Presently there is no general characterization of which polytopal digraphs are LP digraphs, although four necessary properties are known...