This work introduces a novel topological constraint called the intopological digraph space imposed by subbasis ... contains one vertice such that edge ẹ is indegree of it and investigates some properties this structure. Our objective to provide crucial first step in study characteristics digraphs utilizing appropriate topology.

In this work, we design an algorithmic method to associate combinatorial structures with finite-dimensional Malcev algebras. In addition to its theoretical study, we have performed the implementation of procedures to construct the digraph associated with a given Malcev algebra (if its associated combinatorial structure is a digraph) and, conversely, a second procedure to test if a given digraph...

Many interconnection networks can be constructed with line digraph iterations. A digraph has super link-connectivity d if it has link-connectivity d and every link-cut of cardinality d consists of either all out-links coming from a node, or all in-links ending at a node, excluding loop. In this paper, we show that the link-digraph iteration preserves super link-connectivity. c © 2003 Elsevier B...

For any digraph D we construct a digraph s(S) such that D has a k-kernel iff s(S) has a k-kernel. The method employed allows to prove that, any digraph is an induced subdigraph of an infinite set of digraphs with (resp. without) k-kernel; and it can be used as a powerful tool in the construction of a large class of digraphs with (resp. without) k-kernel. Previous results are generalyzed. Mathem...

In this communication, we introduce an original algorithm for computing both dominant and absorbent kernels in a bipolar ordinal valued digraph. The approach relies on theoretical results recently obtained by Bisdorff, Pirlot and Roubens [8] which give a constructive – fixpoint equation based – proof of the bijection between bipolar ordinal valued kernels of such a valued digraph and the crisp ...

Consider a directed graph (digraph) in which vertices are assigned color sets, and two connected if only they share at least one the tail vertex has strictly smaller set than head. We seek to determine smallest possible size of union sets that allows for such digraph representation. To address this problem, we introduce new notion intersection representation digraph, show it is well-defined all...

For a given $2$-partition $(V_1,V_2)$ of the vertices of a (di)graph $G$, we study properties of the spanning bipartite subdigraph $B_G(V_1,V_2)$ of $G$ induced by those arcs/edges that have one end in each $V_i$. We determine, for all pairs of non-negative integers $k_1,k_2$, the complexity of deciding whether $G$ has a 2-partition $(V_1,V_2)$ such that each vertex in $V_i$ has at least $k_i$ ...