A digraph is semicomplete if any two vertices are connected by at least one arc and locally the out-neighbourhood in-neighbourhood of vertex induce a digraph. In this paper we study various subclasses digraphs for which give structural decomposition theorems. As consequence obtain several applications, among an answer to conjecture Naserasr first third authors (Aboulker et al., 2021): oriented ...

In this paper we introduce Digital Probability Hyper Digraph for modeling random variable as the hierarchical data-oriented model. Keywords—Data-Oriented Models, Data Structure, Digital Probability Hyper Digraph, Random Variable, Statistic and Probability.

We show various upper bounds for the order of a digraph (or mixed graph) whose Hermitian adjacency matrix has an eigenspace prescribed codimension. In particular, this generalizes so-called absolute bound (simple) graphs first shown by Delsarte, Goethals, and Seidel (1977) extended Bell Rowlinson (2003). doing so, we also adapt Blokhuis' theory (1983) harmonic analysis in real hyperbolic spaces...

We call the digraph D an m-coloured digraph if its arcs are coloured with m colours. If D is an m-coloured digraph and a ∈ A(D), colour(a) will denote the colour has been used on a. A path (or a cycle) is called monochromatic if all of its arcs are coloured alike. A γ-cycle in D is a sequence of vertices, say γ = (u0, u1, . . . , un), such that ui 6= uj if i 6= j and for every i ∈ {0, 1, . . . ...

Like the Coxeter graph became reattached into the Klein graph in [3], the Levi graphs of the 93 and 103 self-dual configurations, known as the Pappus and Desargues (k-transitive) graphs P and D (where k = 3), also admit reattachments of the distance-(k − 1) graphs of half of their oriented shortest cycles via orientation assignments on their common (k−1)-arcs, concurrent for P and opposite for ...

We introduce and study four optimization problems that generalize the well-known subset sum problem. Given a node-weighted digraph, select a subset of vertices whose total weight does not exceed a given budget. Some additional constraints need to be satisfied. The (weak resp.) digraph constraint imposes that if (all incoming nodes of resp.) a node x belongs to the solution, then the latter comp...

The Directed Maximum Leaf Out-Branching problem is to find an out-branching (i.e. a rooted oriented spanning tree) in a given digraph with the maximum number of leaves. In this paper, we improve known parameterized algorithms and combinatorial bounds on the number of leaves in out-branchings. We show that – every strongly connected digraph D of order n with minimum indegree at least 3 has an ou...