Cut edge vs cut vertices -CONFUSION

[yakin]

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?

 

[Sudharaka]

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.