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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What we have learnt
- Subgraphs are formed by taking a subset of the vertices and edges of a given graph.
- Induced subgraphs focus only on selected vertices and the edges between them.
- Graph isomorphism refers to the structural similarity of two graphs despite possible differences in their representations.
Key Concepts
- -- Subgraph
- A graph formed from a subset of the vertices and edges of another graph.
- -- Induced Subgraph
- A subgraph formed by taking a subset of vertices and including all edges connecting pairs of vertices in that subset.
- -- Graph Isomorphism
- A relation between two graphs that indicates they have the same structure; they can be transformed into each other via a bijection between their vertex sets.
- -- Connectivity
- A property of a graph that indicates whether there exists a path between every pair of distinct vertices.
- -- Cut Vertex
- A vertex whose removal increases the number of connected components in a graph.
- -- Cut Edge
- An edge whose removal increases the number of connected components in a graph.
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