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- What is an Arborescence (Graph Theory)? - Mathematics Stack Exchange
An Arborescence by this definition is synonymous with Directed- (“Generalized Spread” or “Tree-Spread”) In Graph Theory, a Tree allows for connections between nodes, but no cycles
- Arborescence of a graph - Mathematics Stack Exchange
An arborescence in $G$ rooted at $r$ is a subgraph $H$ of $G$ in which every vertex $u \in V \backslash \ {r\}$ has a directed path to the special vertex $r$ The weight of an arborescence $H$ is the sum of the weights of the edges in $H$
- What is an example of a DAG that is *not* an arborescence?
An arborescence is a directed graph where there exists a vertex r (called the root) such that, for any other vertex v, there is exactly one directed walk from r to v (noting that the root r is unique)
- What is the equivalent of a tree for directed graphs?
An arborescence is a tree in which every vertex other than the root has an in-degree of exactly one […] An arborescence is in a sense a tree directed out of the root Therefore an arborescence is sometimes referred to as an out-tree (Reversing the direction of every edge in an arborescence will produce what may be called an in-tree
- A name for this kind of directed tree - Mathematics Stack Exchange
I just discovered that if you reverse all of your edges, you have an arborescence, which according to the article is also called a directed rooted tree, an out-arborescence, and an out-tree
- Number of Spanning Arborescences - Mathematics Stack Exchange
A spanning arborescence with root $x_i$ is a spanning tree $T$ of $G$, with root $x_i$, such that for all $j\ne i$ there is a directed path from $x_j$ to $x_i$ in $T$
- Number of spanning arborescences does not depend on $i$.
An arborescence is a tree with the extra condition that all edges are directed to the root So from $x_i$ there is a unique path to the root, and the first edge of that path is directed out of $x_i$
- A given arboresescence is a shortest path tree if and only if $ d_B (r . . .
An r-arborescence in D is by definition a set of arcs $B \subseteq A$ such that $ (V, B)$ has a unique directed $r -v$ walk, for every $v \in V \setminus {r}$
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