In graphical modelling, a bi-directed graph encodes marginal independences among random variables that are identified with the vertices of the graph (alternatively graphs with dashed edges have been used for this purpose). Bi-directed graphs are special instances of ancestral graphs, which are mixed graphs with undirected, directed, and bi-directed edges. In this paper, we show how simplicial s...

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...

We consider economical representations for the path information in a directed graph. A directed graph G is said to be a transitive reduction of the directed graph G provided that (i) G has a directed path from vertex u to vertex v if and only if G has a directed path from vertex u to vertex v, and (ii) there is no graph with fewer arcs than G satisfying condition (i). Though directed graphs wit...

selecting an effective project plan is a significant area in the project management. the present paper introduces a technique to identify the project plan efficient frontier for assessing the alternative project plans and selecting the best plan. the efficient frontier includes two criteria: the project cost and the project time. besides, the paper presents a scheme to incorporate directed acyc...

The k-th power D of a directed graph D is defined to be the directed graph on the vertices of D with an arc from a to b in D iff one can get from a to b in D with exactly k steps. This notion is equivalent to the k-fold composition of binary relations or k-th powers of Boolean matrices. A k-th root of a directed graph D is another directed graph R with R = D. We show that for each k ≥ 2, comput...

Given a directed graph, there exists a universal operator algebra and universal C-algebra associated to the directed graph. In this paper we give intrinsic constructions of these objects. We provide an explicit construction for the maximal C-algebra of an operator algebra. We also discuss uniqueness of the universal algebras for finite graphs, showing that for finite graphs the graph is an isom...

A directed dominating set in a directed graph D is a set S of vertices of V such that every vertex u ∈ V (D) \ S has an adjacent vertex v in S with v directed to u. The directed domination number of D, denoted by γ(D), is the minimum cardinality of a directed dominating set in D. The directed domination number of a graph G, denoted Γd(G), which is the maximum directed domination number γ(D) ove...