Definition:Loop (Graph Theory)

This page is about Loop in the context of Graph Theory. For other uses, see Loop.

Definition

Let $G = \struct {V, E}$ be a loop-graph.

A loop is an edge $e$ of $G$ whose endvertices are the same vertex.

Thus a loop $e$ on the vertex $v$ would be written:

$e = vv$

Also known as

Some authors refer to a loop $e = vv$ as a self-loop at vertex $v$.

Also see

• Results about loops in the context of graph theory can be found here.

Sources

• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Chapter $1$: Mathematical Models: $\S 1.6$: Networks as Mathematical Models
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): graph: 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): graph: 2.
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): loop