Consequently, each term in (v_{k}bar{beta}_{kj}) is the weight (w(Q)) of a unicyclic subgraph Q of (mathcal{G}) obtained from such a tree T by adding a directed arc ((k,j)) from vertex k to vertex j.
A two-way dependency relationship between attributes in two different clusters was called inter-dependency, denoted by a two-way directed arc between the clusters.
In this paper, a 3D feather-like AlN nanostructure has been prepared by a direct arc discharge method [5, 9, 15] without any catalyst or template, and an alternating growth mechanism is introduced to understand the novel nanostructure.
This instance can be transformed into a bidirected instance (V, A) as follows (cf. [43]): Replace core edges e ∈ E with e = { i, j }, i, j ∈ S by two directed arcs ij ∈ A and ji ∈ A with cost c ij = c ji = c e. Since we are modeling an arborescence directed away from the root node, edges { r, j } are replaced by a single arc rj only.
Each directed arc connects a secondary user to a primary user.
It will be convenient to replace, in the given phylogenetic tree T , every edge e = { v, w} by a pair of directed arcs (v, w) and (w, v) and put λ v, w) = λ w, v):= λ e) (see Figure 1 for an example).
We define the oriented graph G ⪯ in X as follows: the vertices of G ⪯ are the elements of X, and two vertices x, y ∈ X are connected by a directed edge (arc) if x ⪯ y.
A path of length l in G is a sequence v p 1,…, v p i, v p i +1,…, v p l of l nodes, where each pair v p i, v p i +1 of consecutive nodes is connected by a directed edge (arc), which starts in v p i and ends in v p i +1.
Places and transitions are connected by directed arcs: arcs can only link a place to a transition or a transition to a place.
