Cut edge vs cut vertices -CONFUSION

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SUMMARY

This discussion clarifies the concepts of cut edges and cut vertices in graph theory. A cut edge, or bridge, is defined as an edge whose removal increases the number of connected components in the graph. Conversely, a cut vertex is a vertex whose removal also increases the number of connected components. Understanding these definitions is crucial for analyzing graph connectivity and structure.

PREREQUISITES
  • Basic understanding of graph theory concepts
  • Familiarity with connected components in graphs
  • Knowledge of graph representation (e.g., adjacency list or matrix)
  • Ability to visualize graphs and their properties
NEXT STEPS
  • Study algorithms for finding cut edges in graphs, such as Tarjan's algorithm
  • Learn about depth-first search (DFS) and its application in identifying cut vertices
  • Explore the concept of biconnected components in graph theory
  • Investigate practical applications of cut edges and cut vertices in network design
USEFUL FOR

This discussion is beneficial for computer scientists, mathematicians, and software engineers interested in graph theory, particularly those working on network analysis and connectivity problems.

yakin
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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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