Cycle in graph theory and computer science has several meanings: A diagram of a graph with 6 vertices and 7 edges. ... Wikibooks Wikiversity has more about this subject: School of Computer Science Open Directory Project: Computer Science Downloadable Science and Computer Science books Collection of Computer Science Bibliographies Belief that title science in computer science is inappropriate Categories: Wikipedia articles needing priority cleanup | Computer science ...
A closed walk, with repeated vertices allowed. See path (graph theory). (This usage is common in computer science. In graph theory it is more often called a closed walk.)
A closed (simple) path, with no other repeated vertices than the starting and ending vertices. (This usage is common in graph theory.) This may also be called a simple cycle, circuit, circle, or polygon.
A closed directed walk, with repeated vertices allowed. (This usage is common in computer science. In graph theory it is more often called a closed directed walk.)
A closed directed (simple) path, with no repeated vertices other than the starting and ending vertices. (This usage is common in graph theory.) This may also be called a simple (directed) cycle.
The edge set of an undirected closed path without repeated vertices. This may also be called a circuit, circle, or polygon.
An element of the binary or integral (or real, complex, etc.) cycle space of a graph. (This is the usage closest to that in the rest of mathematics, in particular algebraic topology.) Such a cycle may be called a binary cycle, integral cycle, etc.
An edge set which has even degree at every vertex; also called an even edge set or, when taken together with its vertices, an even subgraph. This is equivalent to a binary cycle, since a binary cycle is the characteristic function of an edge set of this type.
In mathematics, a path in a graph is a sequence of vertices such that from each of its vertices there is an edge to the successor vertex. ... // The binary cycle space In graph theory, certain vector spaces over the two-element field Z2 are associated with an undirected graph; this allows one to use the tools of linear algebra to study graphs. ... Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces. ... Some mathematicians use the phrase characteristic function synonymously with indicator function. ...
In the mathematical field of graph theory a cycle graph or circle graph is a graph that consists of a cycle. ... In mathematics, a path in a graph is a sequence of vertices such that from each of its vertices there is an edge to the successor vertex. ...
Traditionally, a cycle in a graph consisted of a sequence of successively incident edges and their endvertices, where the terminating vertices are identical.
A subtree of the graph G is a subgraph that is a tree.
A k-factorable graph is a graph that admits a k-factorization.
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