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

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.

21 sections

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Sections

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  1. 4.1
    Discrete Mathematics

    This section explores key concepts of graph theory, particularly focusing on...

  2. 4.1.1
    Prof. Ashish Choudhury

    This section discusses graph theory concepts including vertex connectivity,...

  3. 4.1.2
    International Institute Of Information Technology - Bangalore

    This section covers the construction of graphs with specific vertex and edge...

  4. 4.1.3
    Lecture - 53

    This section discusses constructing simple graphs based on vertex...

  5. 4.1.4
    Tutorial 9: Part I

    This section discusses the construction of simple graphs based on vertex and...

  6. 4.2

    This section presents a construction of a simple graph based on given...

  7. 4.2.1
    Introduction To Graph Construction

    This section introduces the fundamentals of graph construction, focusing on...

  8. 4.2.2
    Graph Construction Details

    This section outlines how to construct a simple graph based on given vertex...

  9. 4.3

    This section explores the characteristics of a simple graph and the...

  10. 4.3.1
    Unknown Graph G

    This section explores the construction of simple graphs satisfying specific...

  11. 4.3.2
    Edge Set Cardinality

    This section discusses the cardinality of the edge set in graphs and the...

  12. 4.4

    This section explores the construction of a simple non-complete graph that...

  13. 4.4.1
    Connected Non-Complete Graph

    This section discusses the construction of connected non-complete graphs...

  14. 4.5

    This section discusses the Cartesian product of two graphs, defining how it...

  15. 4.5.1
    Cartesian Product Of Graphs

    This section discusses the Cartesian product of graphs, focusing on its...

  16. 4.5.2
    Degree Of Vertices In Cartesian Product

    This section discusses the properties of the degree of vertices in the...

  17. 4.6

    This section discusses the vertex chromatic number in relation to the union...

  18. 4.6.1
    Vertex Chromatic Number

    This section discusses the vertex chromatic number of graphs and...

  19. 4.7
    Combinatorial Proof

    This section discusses the construction of graphs based on vertex and edge...

  20. 4.7.1
    Counting Argument

    This section focuses on constructing simple graphs based on vertex...

  21. 4.8

    In the conclusion, we revisit the key concepts discussed in the chapter,...

What we have learnt

  • Graphs can be constructed based on specific vertex and edge connectivity requirements.
  • The relationship between vertex connectivity, edge connectivity, and minimum degree is critical in graph construction.
  • The Cartesian product of graphs allows for the combination of vertex sets and edge definitions from two separate graphs.

Key Concepts

-- Vertex Connectivity
The minimum number of vertices that must be removed to disconnect the remaining vertices from each other.
-- Edge Connectivity
The minimum number of edges that need to be removed to render the graph disconnected.
-- Cartesian Product of Graphs
A graph operation that creates a new graph whose vertex set consists of ordered pairs of vertices from the original two graphs, with edges defined based on specific connectivity conditions.

Additional Learning Materials

Supplementary resources to enhance your learning experience.