Loop

Definition

A loop is an edge in a graph that connects a vertex to itself. It contributes to the degree of the vertex by two.

5 Must Know Facts For Your Next Test

1. A graph can have multiple loops at the same vertex.
2. Loops are considered when calculating the degree of a vertex.
3. In simple graphs, loops are not allowed.
4. The presence of a loop affects properties like connectivity and Eulerian paths.
5. Loops do not contribute to the concept of bipartite graphs.

Review Questions

• What is the effect of a loop on the degree of a vertex?
• Are loops allowed in simple graphs?
• How does a loop affect the connectivity of a graph?

Related terms

Edge: A connection between two vertices in a graph.

Vertex: A fundamental unit represented as a point in a graph.

Degree: The number of edges incident to a vertex, with loops counted twice.