MHB Cut edge vs cut vertices -CONFUSION

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Cut edges, or bridges, are edges in a graph whose removal increases the number of connected components, while cut vertices are vertices whose removal has the same effect. Identifying a cut edge involves checking if its deletion disconnects the graph, resulting in more connected components. Similarly, a cut vertex can be found by determining if its removal leads to an increase in connected components. Visual aids, such as diagrams, can help clarify the distinction between cut edges and cut vertices. Understanding these concepts is crucial for analyzing graph connectivity.
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How to find if a graph has a cut-edge/bridge and cut vertices. In other words, i am mixed up between cut edge and cut vertices? What is the difference and how one can find these in a graph?
 
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yakin said:
How to find if a graph has a cut-edge/bridge and cut vertices. In other words, i am mixed up between cut edge and cut vertices? What is the difference and how one can find these in a graph?

Hi yakin, :)

Cut edges are edges when deleted increases the number of connected components in the graph. That is by deleting a cut edge you will disconnect the graph into $n+k$ connected components where $n$ is the current number of connected components and $k$ is an integer which depends on the cut edge you remove. Similarly a cut vertex is a vertex when deleted increases the number of connected components in the graph. Here is a picture depicting cut edges and cut vertices. The cut edges are marked in red and the cut vertices are marked in black.

23nxw4.png
 
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