We present two algorithms for maintaining the topological order of a directed acyclic graph with n vertices, under an online edge insertion sequence of m edges. Efficient algorithms for online topological ordering have many applications, including online cycle detection, which is to discover the first edge that introduces a cycle under an arbitrary sequence of edge insertions in a directed grap...

objectives: goal-directed subsidies because of its nature can affect all aspects of iranian life. this scheme is not only an economic program but also affects other aspects of social life including: welfare and economic situation of society, labor market, income, expenditure and consumption pattern models of family and social problems such as poverty and inequality, drug abuse, family problem, ...

introduction: working in the complex and ever changing healthcare settings forces the nurses and nursing students to be equipped with lifelong learning skills. one of the lifelong learning skills is self-directed learning. this study aimed to explore the m.sc. nursing students’ self-directed learning activities. methods: a qualitative design using conventional content analysis approach was used...

the colorful paths and rainbow paths have been considered by severalauthors.a colorful directed path in a digraph $g$ is a directed path with $chi(g)$ vertices whose colors are different. a $v$-colorful directed path is such a directed path, starting from $v$. we prove that for a given $3$-regular triangle-free digraph $g$ determining whether there is a proper $chi(g)$-coloring of $g$such that ...

In a recent Combinatorics seminar, David A. Jackson introduced the following family of directed graphs {Γn}: Let n ∈ N. The vertex set is V (Γn) = Z/nZ. The directed edge (x, y) ∈ E(Γn) if and only if y = x. We allow loops and double edges. In particular, for any n, the edges (0, 0) and (1, 1) belong to E(Γn). As for double edges, (2, 4) and (4, 2) are both in E(Γ7). Γn consists of some number ...

In this paper, we prove the following sufficient condition for the existence of k-kernels in digraphs: Let D be a digraph whose asymmetrical part is strongly conneted and such that every directed triangle has at least two symmetrical arcs. If every directed cycle γ of D with `(γ) 6≡ 0(mod k), k ≥ 2 satisfies at least one of the following properties: (a) γ has two symmetrical arcs, (b) γ has fou...

We examine some properties of the 2-variable greedoid polynomial f(G;t, z) when G is the branching greedoid associated to a rooted graph or a rooted directed graph. For rooted digraphs, we show a factoring property of f (G;t ,z) determines whether or not the rooted digraph has a directed cycle.

We review the Manhattan product of digraphs from the viewpoint of spectral analysis and obtain some preliminary formulae. As an example, the spectrum of the Manhattan product of the directed path Pn and the directed cycle C2 is obtained as well as its asymptotic spectral distribution.

The cycle space of a strongly connected graph has a basis consisting of directed circuits. The concept of relevant circuits is introduced as a generalization of the relevant cycles in undirected graphs. A polynomial time algorithm for the computation of a minimum weight directed circuit basis is outlined.