In graph theory, a cycle graph or circular graph is a graph that consists of a single cycle, or in other words, some number of vertices (at least 3, if the graph is simple) connected in a closed chain.

4 days ago · In graph theory, a cycle graph , sometimes simply known as an -cycle (Pemmaraju and Skiena 2003, p. 248), is a graph on nodes containing a single cycle through all nodes.

Jul 23, 2025 · A cyclic graph is defined as a graph that contains at least one cycle which is a path that begins and ends at the same node, without passing through any other node twice.

Jul 12, 2025 · We can call a graph as a cycle graph if there is the same starting and last vertex, but there should not be any repeated edges.

Mar 18, 2024 · A cycle consists of a sequence of adjacent and distinct nodes in a graph. The only exception is that the first and last nodes of the cycle sequence must be the same node.

We call a graph acyclic if it contains no cycles. The next theorem is useful to determine whether an edge is a cut edge by checking that if it is contained in any cycles.

May 19, 2025 · A cycle in graph theory is defined as a path of edges and vertices wherein a vertex is reachable from itself while traversing through a sequence of distinct nodes (except for the repeated …

Aug 17, 2025 · Some sources specify that a cycle must indeed have at least $3$ edges, presupposing that the graph in which it is embedded is by definition a simple graph. Some sources refer to a cycle …

Since the graph is made up of a bunch of cycles, each vertex has an option: to be in each cycle, or not. If it's in a particular cycle (for example, in the red cycle), that cycle contributes two edges to its …

Jul 7, 2021 · A cycle is like a path, except that it starts and ends at the same vertex. The structures that we will call cycles in this course, are sometimes referred to as circuits.