Definition:Circuit (Graph Theory)

Definition

A circuit is a closed trail with at least one edge.

Subgraph

The set of vertices and edges which go to make up a circuit form a subgraph.

This subgraph itself is also referred to as a circuit.

Also defined as

Some sources specifically state that a circuit must have at least $3$ edges.

However, as defined on $\mathsf{Pr} \infty \mathsf{fWiki}$, this criterion emerges as a consequence of the definition.

Also known as

Some sources refer to a circuit as a closed trail.

Also see

• Circuit of Simple Graph has Three Edges or More

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

Sources

• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): $\S 2.3$: Connected Graphs
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): circuit
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): walk
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): circuit
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): walk
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): closed (in graph theory)