Discrete Mathematics - Vol 3 | 4. Prof. Ashish Choudhury by Abraham | Learn Smarter
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4. Prof. Ashish Choudhury

The tutorial focuses on advanced graph theory concepts, particularly pertaining to vertex connectivity, edge connectivity, and overall graph construction using complete graphs. It elaborates on real-world applications through various problems, demonstrating how to construct graphs based on given connectivity constraints and exploring the Cartesian product of graphs. Additionally, it discusses coloring principles in graph theory and challenges assumptions regarding the properties of graph unions.

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Sections

  • 4.1

    Discrete Mathematics

    This section explores key concepts of graph theory, particularly focusing on graph connectivity metrics including vertex connectivity, edge connectivity, and minimum degree.

    Learning Practice

  • 4.1.1

    Prof. Ashish Choudhury

    This section discusses graph theory concepts including vertex connectivity, edge connectivity, and minimum degree, exploring how to construct graphs based on given conditions.

    Learning Practice

  • 4.1.2

    International Institute Of Information Technology - Bangalore

    This section covers the construction of graphs with specific vertex and edge connectivity characteristics, as well as exercises for understanding these concepts.

    Learning Practice

  • 4.1.3

    Lecture - 53

    This section discusses constructing simple graphs based on vertex connectivity, edge connectivity, and minimum degree while also exploring graph properties and operations.

    Learning Practice

  • 4.1.4

    Tutorial 9: Part I

    This section discusses the construction of simple graphs based on vertex and edge connectivity requirements, as well as analyzing a simple graph with specific properties.

    Learning Practice

  • 4.2

    Question 1

    This section presents a construction of a simple graph based on given parameters related to vertex and edge connectivity, and minimum degree.

    Learning Practice

  • 4.2.1

    Introduction To Graph Construction

    This section introduces the fundamentals of graph construction, focusing on vertex connectivity, edge connectivity, and minimum degree.

    Learning Practice

  • 4.2.2

    Graph Construction Details

    This section outlines how to construct a simple graph based on given vertex connectivity, edge connectivity, and minimum degree constraints.

    Learning Practice

  • 4.3

    Question 2

    This section explores the characteristics of a simple graph and the implications of deleting vertices on the cardinality of the edge set.

    Learning Practice

  • 4.3.1

    Unknown Graph G

    This section explores the construction of simple graphs satisfying specific connectivity and degree conditions using given positive integers.

    Learning Practice

  • 4.3.2

    Edge Set Cardinality

    This section discusses the cardinality of the edge set in graphs and the relationships between various connectivity measures like vertex connectivity and edge connectivity.

    Learning Practice

  • 4.4

    Question 3

    This section explores the construction of a simple non-complete graph that has equal vertex connectivity, edge connectivity, and minimum degree.

    Learning Practice

  • 4.4.1

    Connected Non-Complete Graph

    This section discusses the construction of connected non-complete graphs characterized by specific connectivity parameters.

    Learning Practice

  • 4.5

    Question 4

    This section discusses the Cartesian product of two graphs, defining how it operates and proving the cardinality of the resulting edge set.

    Learning Practice

  • 4.5.1

    Cartesian Product Of Graphs

    This section discusses the Cartesian product of graphs, focusing on its construction, properties, and significance in graph theory.

    Learning Practice

  • 4.5.2

    Degree Of Vertices In Cartesian Product

    This section discusses the properties of the degree of vertices in the Cartesian product of two graphs, including how degree, vertex connectivity, and edge connectivity interrelate.

    Learning Practice

  • 4.6

    Question 5

    This section discusses the vertex chromatic number in relation to the union of two graphs, providing a counterexample that disproves a commonly intuitively held belief.

    Learning Practice

  • 4.6.1

    Vertex Chromatic Number

    This section discusses the vertex chromatic number of graphs and relationships between vertex connectivity, edge connectivity, and minimum degree.

    Learning Practice

  • 4.7

    Combinatorial Proof

    This section discusses the construction of graphs based on vertex and edge connectivity, and how combinatorial proofs help in understanding graph properties.

    Learning Practice

  • 4.7.1

    Counting Argument

    This section focuses on constructing simple graphs based on vertex connectivity, edge connectivity, and minimum degree, utilizing various properties and relationships between these graph characteristics.

    Learning Practice

  • 4.8

    Conclusion

    In the conclusion, we revisit the key concepts discussed in the chapter, emphasizing the relationships between vertex connectivity, edge connectivity, and minimum degree in graphs.

    Learning Practice

References

ch54.pdf

Class Notes

Memorization

What we have learnt

  • Graphs can be constructed b...
  • The relationship between ve...
  • The Cartesian product of gr...

Final Test

Revision Tests