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A directed acyclic graph is a directed graph that has no cycles. [1] [2] [3] A vertex v of a directed graph is said to be reachable from another vertex u when there exists a path that starts at u and ends at v. As a special case, every vertex is considered to be reachable from itself (by a path with zero edges).
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 ...
DAG Abbreviation for directed acyclic graph, a directed graph without any directed cycles. deck The multiset of graphs formed from a single graph G by deleting a single vertex in all possible ways, especially in the context of the reconstruction conjecture. An edge-deck is formed in the same way by deleting a single edge in all possible ways.
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 ...
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 ...
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 ...
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 ...
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.