In k-Digraph Coloring we are given a digraph and asked to partition its vertices into at most k sets, so that each set induces DAG. This well-known problem is NP-hard, as it generalizes (undirected) k-Coloring, but becomes trivial if the input acyclic. poses natural parameterized complexity question of what happens when “almost” this paper study using parameters measure input’s distance acyclic...

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 ...

Many interconnection networks can be constructed with line digraph iterations. In this paper, we will establish a general result on super line-connectivity based on the line digraph iteration which improves and generalizes several existing results in the literature.

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.