This paper presents an algorithm for the shortest-path problem on a directed graph having arbitrary arc weights. One feature of the algorithm is its ability to exploit a certain type of structure. Two examples of this feature are highlighted. The rst example is when the given graph is “almost” acyclic in the sense that there exists a small subset T of nodes, the deletion of which yields an acyc...

understanding cattle metabolism and its relationship with milk products is important in bovine breeding. a systemic view could lead to consequences that will result in a better understanding of existing concepts. topological indices and quantitative characterizations mostly result from the application of graph theory on biological data. in the present work, the enzyme network involved in cattle...

Let H = (V (H), A(H)) be a digraph possibly with loops and D = (V (D), A(D)) a digraph whose arcs are colored with the vertices of H (this is what we call an H-colored digraph); i.e. there exists a function c : A(D) → V (H); for an arc of D, f = (u, v) ∈ A(D), we call c(f) = c(u, v) the color of f . A directed walk (directed path) P = (u0, u1, . . . , un) in D will be called an H-walk (H-path) ...

Given a directed graph G = (V;E), a natural problem is to choose a minimum number of the edges in E such that, for any two vertices u and v, if there is a path from u to v in E, then there is a path from u to v among the chosen edges. We show that in graphs having no directed cycle with more than three edges, this problem is equivalent to Maximum Bipartite Matching. This leads to a small improv...

A strongly connected digraph is called a cactoid-type if each of its blocks consisting finitely many oriented cycles sharing common directed path. In this article, we find...

We begin with trying to find the shortest path in a directed acyclic graph (DAG). Recall that a DAG has directed edges and contains no cycles. Recall the definition of a topological sort: Definition 1. Let G = (V,E) be a graph. Let v1, . . . ,vn be an ordering of the vertices in V . v1, . . . ,vn are in topologically sorted order if for all edges (vi,v j) ∈ E, i < j. If G is a DAG, then it is a...

In recent years, the study of directed complex network is becoming a hot issue. Complex networks describe a wide range of systems. In this paper, based on the complex network theory, we find that supply chain network is clearly not a random network but a directed scale-free network. Statistic characteristics of the network model such as degree distribution, supply chain average shortest path an...

XPath is a very natural and powerful way to specify locations in XML documents. This paper examines possible generalizations of XPath to allow both locations and paths through generalized labeled directed graphs to be specified. The need for such a path language is driven by work in querying Linguistic Annotations which are in general more complex in structure than XML documents. The result of ...

A digraph D is unilateral if for every pair x, y of its vertices there exists a directed path from x to y, or a directed path from y to x, or both. A mixed graph M = (V,A,E) with arc-set A and edgeset E accepts a unilateral orientation, if its edges can be oriented so that the resulting digraph is unilateral. In this paper, we present the first linear-time recognition algorithm for unilaterally...

Let D be a digraph. V (D) denotes the set of vertices of D; a set N ⊆ V (D) is said to be a k-kernel of D if it satisfies the following two conditions: for every pair of different vertices u, v ∈ N it holds that every directed path between them has length at least k and for every vertex x ∈ V (D) − N there is a vertex y ∈ N such that there is an xy-directed path of length at most k − 1. In this...