Definition:Connected (Graph Theory)
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This page is about Connected in the context of Graph Theory. For other uses, see 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
- Results about connectedness in the context of graph theory can be found here.