Category:Definitions/Connectedness (Graph Theory)

This category contains definitions related to connectedness in the context of graph theory.
Related results can be found in Category:Connectedness (Graph Theory).

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.