What is the definition of a connected graph in an undirected graph?
Conditions
- The graph is undirected.
- The criterion for judgment is whether a path exists between any two vertices.
Reasoning, step by step
- Identify the graph as an undirected graph.
- Check if there is a path between every pair of vertices.
- If a path exists for all pairs, the graph is connected.
- If at least one pair lacks a path, the graph is disconnected.
Example
In the example graph, although there is no direct edge between vertices A and D, there exists a path A-C-D. Therefore, A and D are connected, and the graph is a connected graph.
Common misconceptions
- Believing that two vertices must be joined by a direct edge to be connected.
- Confusing the concept of a path with the concept of an edge.
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