What Is a Directed Cycle

A directed cycle is a directed path (with at least one edge) whose first and last vertices are the same. A directed cycle is simple if it has no repeated vertices (other than the requisite repetition of the first and last vertices). The length of a path or a cycle is its number of edges.

What is a directed cycle in a graph?

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.

What is a simple cycle?

A simple cycle is a cycle with no repeated vertices (except for the beginning and ending vertex). Remark: If a graph contains a cycle from v to v, then it contains a simple cycle from v to v. … Connected Graphs. A graph G is called connected if there is a path between any two distinct vertices of G.