What is a cyclic graph?

A cyclic graph is a graph containing at least one graph cycle. A graph that is not cyclic is said to be acyclic . A cyclic graph possessing exactly one (undirected, simple) cycle is called a unicyclic graph . Cyclic graphs are not trees . A cyclic graph is bipartite iff all its cycles are of even length (Skiena 1990, p. 213).

What is acyclic graph in Wolfram?

(OEIS A000055 ). A graph can be tested in the Wolfram Language to see if it is acyclic using AcyclicGraphQ [ g ], and a collection of acyclic graphs are available as GraphData [ "Acyclic" ]. A graph with a single cycle is known as a unicyclic graph .

Is a directed graph acyclic?

Associated with every digraph is its underlying graph which is an undirected graph with the same vertex and edge set but "ignoring" the direction. So when we say that a directed graph is or isn't acyclic, we are implicitly referring to whether the underlying graph is acyclic.

What is an undirected cyclic graph?

In an undirected cyclic graph, the edges have no direction, and the cycle can go in any direction. A cyclic graph may have multiple cycles of different lengths and shapes. Some cycles may be contained within other cycles. A cyclic graph is bipartite if and only if all its cycles are of even length.