Discrete Mathematics - Vol 2 | 28. Vertex and Edge Connectivity by Abraham | Learn Smarter
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Knowledge
28. Vertex and Edge Connectivity

The lecture discusses vertex connectivity and edge connectivity within graph theory, explaining how vertex cuts and edge cuts relate to the disconnection of a graph. It introduces the definitions of vertex connectivity, edge connectivity, and their respective measures, as well as the relationship between them. Special cases such as complete graphs are explored, establishing key insights into how these connectivity measures operate in various structures.

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Sections

  • 28.1

    Discrete Mathematics

    This section discusses vertex connectivity, edge connectivity, vertex cuts, and edge cuts in graphs.

    Learning Practice

  • 28.1.1

    Vertex And Edge Connectivity

    This section discusses the definitions of vertex and edge connectivity in graphs, including vertex cuts, edge cuts, and their relationships.

    Learning Practice

  • 28.1.2

    Definition Of A Vertex Cut

    A vertex cut in graph theory refers to a proper subset of vertices whose removal disconnects the graph.

    Learning Practice

  • 28.1.3

    Vertex Connectivity Of A Graph

    This section explores vertex connectivity in graphs, defining key concepts such as vertex cuts, connectivity, and their relationships with edge connectivity.

    Learning Practice

  • 28.1.4

    Edge Cut

    The section discusses edge cuts and edge connectivity in graphs, defining key concepts and their importance in graph theory.

    Learning Practice

  • 28.1.5

    Edge Connectivity Of A Graph

    This section discusses the concepts of vertex and edge connectivity in graphs, defining key terms, providing examples, and explaining their significance.

    Learning Practice

  • 28.1.6

    Upper Bounds On Vertex Connectivity And Edge Connectivity

    This section discusses vertex cuts, vertex connectivity, edge cuts, and edge connectivity, establishing their definitions and their relationships, specifically for connected, non-complete graphs.

    Learning Practice

  • 28.1.7

    Relationship Between Vertex Connectivity And Edge Connectivity

    This section defines vertex and edge connectivity in graphs and proves their interrelationship, showcasing how they are influenced by the graph's structure.

    Learning Practice

  • 28.1.8

    Conclusion

    This conclusion summarizes the concepts of vertex and edge connectivity, highlighting their definitions, properties, and relationships.

    Learning Practice

References

ch49.pdf

Class Notes

Memorization

What we have learnt

  • Vertex cuts disconnect a gr...
  • Edge cuts disconnect a grap...
  • Vertex connectivity is alwa...

Final Test

Revision Tests