|
Cyclic Graph
In mathematics, a cyclic graph may mean a graph that contains a cycle, or a graph that is a cycle, with varying definitions of cycles. See: *Cycle (graph theory), a cycle in a graph *Forest (graph theory), an undirected graph with no cycles *Biconnected graph, an undirected graph in which every edge belongs to a cycle *Directed acyclic graph, a directed graph with no cycles *Strongly connected graph, a directed graph in which every edge belongs to a cycle *Aperiodic graph, a directed graph in which the cycle lengths have no nontrivial common divisor *Pseudoforest, a directed or undirected graph in which every connected component includes at most one cycle *Cycle graph, a graph that has the structure of a single cycle *Pancyclic graph, a graph that has cycles of all possible lengths *Cycle detection (graph theory), the algorithmic problem of finding cycles in graphs Other similarly-named concepts include *Cycle graph (algebra), a graph that illustrates the cyclic subgroups of a group ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cycle (graph Theory)
In graph theory, a cycle in a graph is a non-empty trail in which only the first and last vertices are equal. A directed cycle in a directed graph is a non-empty directed trail in which only the first and last vertices are equal. A graph without cycles is called an ''acyclic graph''. A directed graph without directed cycles is called a ''directed acyclic graph''. A connected graph without cycles is called a ''tree''. Definitions Circuit and cycle * A circuit is a non-empty trail in which the first and last vertices are equal (''closed trail''). : Let be a graph. A circuit is a non-empty trail with a vertex sequence . * A cycle or simple circuit is a circuit in which only the first and last vertices are equal. Directed circuit and directed cycle * A directed circuit is a non-empty directed trail in which the first and last vertices are equal (''closed directed trail''). : Let be a directed graph. A directed circuit is a non-empty directed trail with a vertex sequence ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
