cycle graph
graph that includes every vertex in which every vertex is adjacent to exactly 2 vertices
A cycle graph is a type of graph that consists of vertices arranged in a loop and connected by edges in a circular manner. The cycle graph is also known as a cyclic graph. A cycle graph can be denoted as Cn, where n represents the number of vertices or nodes.
To construct a cycle graph, we start with a circle, which has n nodes, and connect adjacent nodes with edges. The resulting graph will have n nodes and n edges. Since the graph is cyclic, we can also think of the first and last nodes as being adjacent.
The properties of a cycle graph include :
1. All nodes in a cycle graph have the same degree, which is two.
2. A cycle graph with n nodes has n edges.
3. The cycle graph with two nodes is also known as a line graph.
4. The cycle graph is a simple graph, which means there are no loops or multiple edges between nodes.
Cycle graphs can be used to model many real-world situations, such as traffic patterns or the movement of objects in a circular motion. In computer science, cycle graphs are used to model algorithms, data structures, and network topologies.
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