Discrete Mathematics - Vol 2 | 27. Various Operations on Graphs by Abraham | Learn Smarter
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27. Various Operations on Graphs

This chapter covers various operations on graphs, including the definition and properties of subgraphs, induced subgraphs, and data structures for graph representation. Additionally, it discusses the concepts of graph isomorphism and connectivity, as well as critical vertices and edges in graphs. The chapter highlights the importance of these concepts in understanding the structural properties of graphs and their applications.

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Sections

  • 1

    Discrete Mathematics

    This section elaborates on various operations that can be performed on graphs, including subgraphs, proper subgraphs, and induced subgraphs, along with insights on graph isomorphism and connectivity.

    Learning Practice

  • 1.1

    Various Operations On Graphs

    This section covers fundamental operations on graphs, including definitions of subgraphs, proper subgraphs, and induced subgraphs, alongside operations such as edge and vertex deletion.

    Learning Practice

  • 1.2

    Subgraph Of A Graph

    This section discusses the concept of subgraphs in graph theory, including definitions, properties, and operations on graphs.

    Learning Practice

  • 1.3

    Proper Subgraph

    This section defines what constitutes a proper subgraph in graph theory, highlighting its characteristics and relation to induced subgraphs and various graph operations.

    Learning Practice

  • 1.4

    Induced Subgraph

    This section introduces the concept of induced subgraphs, detailing how they are formed from a subset of vertices of a graph.

    Learning Practice

  • 1.5

    Set Theoretic Operations On Graphs

    This section explores various set theoretic operations on graphs, including definitions of subgraphs, proper subgraphs, and induced subgraphs, as well as the significant implications of graph operations.

    Learning Practice

  • 1.6

    Data Structures To Represent Graphs

    This section explores different methods of representing graphs, focusing on structures like adjacency matrices and lists, and discusses graph operations such as subgraphs and isomorphism.

    Learning Practice

  • 1.7

    Graph Isomorphism

    This section explores graph isomorphism, defining subgraphs, induced subgraphs, and their implications in graph theory.

    Learning Practice

  • 1.8

    Graph Connectivity

    This section defines various forms of graph connectivity, including subgraphs, proper subgraphs, induced subgraphs, and concepts of connected graphs and components.

    Learning Practice

  • 1.9

    Cut Vertex And Cut Edge

    This section defines and explores the concepts of cut vertices and cut edges in graphs, highlighting their importance in connectivity.

    Learning Practice

References

ch48.pdf

Class Notes

Memorization

What we have learnt

  • Subgraphs are formed by tak...
  • Induced subgraphs focus onl...
  • Graph isomorphism refers to...

Final Test

Revision Tests