Discrete Mathematics - Vol 1 | 19. Transitive Closure of Relations by Abraham | Learn Smarter
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19. Transitive Closure of Relations

The chapter covers the concept of transitive closure in relations using graphical interpretations. The connectivity relationship is defined, showing how it is constructed through the union of powers of a relation. The naive algorithm for computing this transitive closure is introduced, emphasizing its significance in graph theory and practical applications like social networks.

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Sections

  • 19

    Transitive Closure Of Relations

    The transitive closure of a relation is a mathematical concept that describes the connectivity of elements within a set, allowing for indirect relationships through path lengths.

    Learning Practice

  • 19.1

    Introduction To Connectivity Relation

    This section introduces the connectivity relationship in the context of relations and transitive closures, highlighting its significance and properties.

    Learning Practice

  • 19.2

    The Relationship Between Transitive Closure And Connectivity Relation

    This section explores the concept of transitive closure in relation to connectivity in directed graphs, defining the connectivity relation and proving the relationship between transitive closure and connectivity.

    Learning Practice

  • 19.3

    Proof Of Transitive Closure Properties

    This section discusses the transitive closure of relations, its properties, and how it can be computed through a connectivity relation.

    Learning Practice

  • 19.4

    Significance Of Connectivity Relationship

    The significance of the connectivity relationship in the context of transitive closures of relations is introduced, emphasizing the key algorithmic and graph theoretical aspects.

    Learning Practice

  • 19.5

    Naive Algorithm For Computing Connectivity Relation

    This section presents the naive algorithm for computing the connectivity relation of a given relation, detailing how the transitive closure can be achieved through Boolean matrix operations.

    Learning Practice

References

ch18.pdf

Class Notes

Memorization

What we have learnt

  • The transitive closure of a...
  • A relation R defined over a...
  • Graphical interpretations c...

Final Test

Revision Tests