Search results
Results from the WOW.Com Content Network
In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it consists of vertices and edges (also called arcs ), with each edge directed from one vertex to another, such that following those directions will never form a closed loop.
However, the degree sequence does not, in general, uniquely identify a directed graph; in some cases, non-isomorphic digraphs have the same degree sequence. The directed graph realization problem is the problem of finding a directed graph with the degree sequence a given sequence of positive integer pairs. (Trailing pairs of zeros may be ...
For most graphs, this transformation is not useful because it creates cycles of negative length in −G. But if G is a directed acyclic graph (DAG), then no negative cycles can be created, and a longest path in G can be found in linear time by applying a linear time algorithm for shortest paths in −G, which is also a directed acyclic graph. [4]
For planar graphs, acyclic orientations are dual to totally cyclic orientations, orientations in which each edge belongs to a directed cycle: if is a planar graph, and orientations of are transferred to orientations of the planar dual graph of by turning each edge 90 degrees clockwise, then a totally cyclic orientation of corresponds in this ...
A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees. [2] A directed tree, [3] oriented tree, [4] [5] polytree, [6] or singly connected network [7] is a directed acyclic graph (DAG) whose underlying undirected graph is ...
Chen (1966) gives a characterization for directed multigraphs with a bounded number of parallel arcs and loops to a given degree sequence. The additional constraint of the acyclicity of the directed graph is known as dag realization. Nichterlein & Hartung (2012) proved the NP-completeness of this problem.
In this tree, the lowest common ancestor of the nodes x and y is marked in dark green. Other common ancestors are shown in light green. In graph theory and computer science, the lowest common ancestor (LCA) (also called least common ancestor) of two nodes v and w in a tree or directed acyclic graph (DAG) T is the lowest (i.e. deepest) node that has both v and w as descendants, where we define ...
The degree sequence problem is the problem of finding some or all graphs with the degree sequence being a given non-increasing sequence of positive integers. (Trailing zeroes may be ignored since they are trivially realized by adding an appropriate number of isolated vertices to the graph.) A sequence which is the degree sequence of some simple ...