Discrete Mathematics - Vol 2 | 29. Introduction to Tutorial 8 by Abraham | Learn Smarter
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29. Introduction to Tutorial 8

This chapter delves into fundamental concepts and properties of graphs, including Ramsey numbers, articulation points, trees, self-complementary graphs, and regular graphs. A strong focus is placed on proving or disapproving specific propositions regarding graph properties while providing a theoretical framework for understanding these relationships. Key proofs are reinforced through various exercises and activities, which encourage deeper engagement with the material.

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Sections

  • 29.1

    Discrete Mathematics

    This section explores the properties of simple graphs and concepts related to graph theory, including Ramsey numbers, articulation points, incidence matrices, trees, and self-complementary graphs.

    Learning Practice

  • 29.1.1

    Introduction To Tutorial 8

    This section discusses key concepts in graph theory, including Ramsey numbers, the properties of trees, and self-complementarity in graphs.

    Learning Practice

  • 29.1.2

    Question 1

    The section discusses the properties of a simple graph with 6 nodes, demonstrating that either a complete graph K3 or its complement must exist.

    Learning Practice

  • 29.1.3

    Question 2

    This section discusses the relationship between the disconnection of a graph and the properties of its vertices as articulation points.

    Learning Practice

  • 29.1.4

    Question 3

    In this section, the process of recovering an unknown graph from its incidence matrix product is explored.

    Learning Practice

  • 29.1.5

    Question 4

    This section discusses the properties of trees in graph theory, specifically proving that any tree with n nodes has n - 1 edges through induction.

    Learning Practice

  • 29.1.6

    Question 5

    This section discusses self-complementary graphs and their properties, specifically focusing on the relationship between the number of vertices in such graphs.

    Learning Practice

  • 29.1.7

    Question 6

    Question 6 discusses whether the complement H' of a subgraph H of G must also be a subgraph of the complement G'.

    Learning Practice

  • 29.1.8

    Question 7

    This section introduces concepts of regular graphs and explores examples of different types of regular graphs.

    Learning Practice

  • 29.1.9

    Question 8

    This section explores the construction of a simple regular graph where the degree of each vertex is `2k + 1` and the graph contains a cut edge.

    Learning Practice

  • 29.2

    Graph Theory Concepts

    This section covers basic concepts of graph theory, including definitions of graphs, complements, Ramsey numbers, and their relevance in demonstrating relationships in social networks.

    Learning Practice

  • 29.2.1

    Complement Of A Graph

    This section discusses the concept of graph complements, including definitions and properties relevant to simple graphs with 6 nodes, along with the significance of Ramsay numbers.

    Learning Practice

  • 29.2.2

    Ramsay Numbers

    This section explores Ramsay numbers through the concepts of friendship and graph theory, illustrating that within any group of 6 people, there must exist either three mutual friends or three mutual enemies.

    Learning Practice

  • 29.2.3

    Articulation Points

    This section explores articulation points in graph theory, highlighting their significance in analyzing graph connectivity.

    Learning Practice

  • 29.2.4

    Incidence Matrix

    This section delves into incidence matrices of graphs, illustrating concepts such as graph complements and the connections to Ramsey Theory.

    Learning Practice

  • 29.2.5

    Self-Complementary Graph

    This section explores the concept of self-complementary graphs and their properties, particularly focusing on the conditions related to the number of vertices.

    Learning Practice

References

ch50.pdf

Class Notes

Memorization

What we have learnt

  • The complement of a graph h...
  • For any party with 6 guests...
  • A tree with n nodes possess...

Final Test

Revision Tests