Definition:Connected (Graph Theory)

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This page is about connectedness in graph theory. For other uses, see Definition:Connected.

Definition

Vertices

Let $G$ be a graph.

Two vertices $u, v \in G$ are connected if and only if either:

$(1): \quad u = v$
$(2): \quad u \ne v$, and there exists a walk between them.


Graph

Let $G$ be a graph.

Then $G$ is connected if and only if every pair of vertices in $G$ is connected.


Also see