The computation task of a distributed processing system usually can be partitioned into a set of modules and then modeled as a directed graph, called the task digraph. In the task digraph, vertices represent modules and arcs represent message passing links between two modules. Particularly, according to the logical structures and precedence relationships among modules, a large class of task dig...

W e study node fault-tolerance propert ies of the dary deBruij’n and shufle-exchange networks by appealing t o the algebraic structure of their underlying digraphs. In particular, we prove that both of these families of digraphs have connectivity equal t o their minimum degree. T h i s result is new in the case of the shuffle-exchange digraphs and can be extended f o r both famil ies t o charac...

We derive some Moore-like bounds for multipartite digraphs, which extend those of bipartite digraphs, assuming that every vertex of a given partite set is adjacent to the same number of vertices (δ) in each of the other independent sets. We determine when a Moore multipartite digraph is weakly distanceregular. Within this framework, some necessary conditions for the existence of a Moore r-parti...

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 characterized and the structure of non-strong 3-transitive digraphs is described. The results are used, e.g...

Ž . The initial structural models based on balance theory structural balance and clusterability dealt with Ž . incomplete signed digraphs. However, newer models ranked clusters, transitivity, hierarchical M-cliques apply only to zero-one matrices representing either unsigned digraphs or complete signed digraphs. Since empirical networks of affective relations are signed but seldom complete — ac...

1 . Introduction . In this paper we shall consider multigraphs and digraphs (= directed graphs) with bounded multiplicity : an integer r is fixed and we shall assume, that the considered multigraphs or digraphs have no loops, further, if u and v are two vertices of a multigraph M, they can be joined by more than one edge, however, they cannot be joined by more than r edges. In case of digraphs ...

We revisit the deadlock-prevention problem by focusing on priority digraphs instead of the traditional wait-for digraphs. This has allowed us to formulate deadlock prevention in terms of prohibiting the occurrence of directed cycles even in the most general of wait models (the so-called AND-OR model, in which prohibiting wait-for directed cycles is generally overly restrictive). For a particula...

In many papers, the relation between the domination number of a product of graphs and the product of domination numbers of factors is studied. Here we investigate this problem for domination and total domination numbers in the cross product of digraphs. We give analogues of known results for graphs, and we also present new results for digraphs with sources. Using these results we find dominatio...

Seymour’s second neighborhood conjecture states that every simple digraph (without digons) has a vertex whose first out-neighborhood is at most as large as its second out-neighborhood. Such a vertex is said to have the second neighborhood property (SNP). We define ”good” digraphs and prove a statement that implies that every feed vertex of a tournament has the SNP. In the case of digraphs missi...

We propose a quantum walk defined by digraphs (mixed graphs). This is like Grover that perturbed certain complex-valued function digraphs. The discriminant of this matrix normalization generalized Hermitian adjacency matrices. Furthermore, we give definitions the positive and negative supports transfer matrix, clarify explicit formulas their square. In addition, tables computer on identificatio...