Graph Theory/Connectivity
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This page may need to be Whether or not it is possible to traverse a graph from one vertex to another is dependent on how connected a graph is.
[edit] Definition of Connectedness
- If there is a u-v path in G, then we say that u and v are connected
- If there is a u-v path for every pair of vertices u and v in G, then we say that G is connected
[edit] Theorems on Connectedness
Theorem: Let G be a graph of order at least 3. If there are distinct vertices u and v in G so that G-u and G-v are both connected, then G is also connected. Proof: to be completed
