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).

Unfortunately, the term "cyclic graph" is sometimes also used in several other distinct and mutually incompatible ways in mathematics, especially outside graph theory. It is for example sometimes used to mean a Hamiltonian graph, a graph isomorphic to a cycle graph C_n, or a cycle graph itself (Trudeau 1994). Some care is therefore needed when consulting the literature.

See also

Acyclic Graph, Cycle Graph, Forest, Graph Cycle, Hamiltonian Graph, k-Cyclic Graph Star Graph, Tree, Unicyclic Graph, Wheel Graph

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References

Balaban, A. T. "Enumeration of Cyclic Graphs." In Chemical Applications of Graph Theory (Ed. A. T. Balaban). London: Academic Press, pp. 63-105, 1976.Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, 1990.Trudeau, R. J. Introduction to Graph Theory. New York: Dover, 1994.

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Cyclic Graph

Cite this as:

Weisstein, Eric W. "Cyclic Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CyclicGraph.html

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