VTU Notes | 18CS32 - DATA STRUCTURES AND APPLICATIONS

Graphs

Module-5

4.9
2018 Scheme | CSE Department

Created by VtuNotes.in
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5 Modules

18CS32 - DATA STRUCTURES AND APPLICATIONS | Module-5 VTU Notes

VTU | 18CS32 | Module - 5

Graphs, Representations, Operations, and Traversal Methods

This summary outlines the core concepts of graphs, their representations, elementary operations, and traversal methods, as covered in the "Data Structures and Applications" course.

Graphs: Definitions and Terminology:

Graphs are collections of nodes (vertices) connected by edges. Key terms include directed and undirected graphs, weighted and unweighted edges, and paths.

Matrix and Adjacency List Representation:

Graphs can be represented using an adjacency matrix (2D array) or an adjacency list (array of lists). Matrices are suitable for dense graphs, while lists are efficient for sparse graphs.

Elementary Graph Operations:

- Adding a Vertex: Incorporate a new vertex into the graph.

- Adding an Edge: Establish a connection between two vertices.

- Removing a Vertex or Edge: Eliminate a vertex or edge from the graph.

- Checking Connectivity: Determine if two vertices are connected.

- Finding Degree: Count the number of edges connected to a vertex.

Traversal Methods: Breadth-First Search (BFS) and Depth-First Search (DFS):

- BFS: Explore graph level by level, starting from a selected vertex. Useful for shortest path algorithms.

- DFS: Traverse as deeply as possible before backtracking. Useful for searching and pathfinding.

Examples:

1. Graph Representation: Illustrate an undirected graph with nodes A, B, C, and D, connected by edges with varying weights.

2. Adjacency Matrix: Show the adjacency matrix representation of the graph in example 1.

3. Adjacency List: Display the adjacency list representation of the same graph, highlighting relationships.

4. BFS Traversal: Demonstrate BFS traversal on the graph, starting from vertex A and listing visited nodes.

5. DFS Traversal: Illustrate DFS traversal on the same graph, starting from vertex A and listing visited nodes.

Conclusion:

Graphs are versatile structures with applications in various domains, from social networks to transportation systems. Understanding their definitions, representations, operations, and traversal methods is pivotal. Through examples and practical exercises, students solidify their comprehension of graph manipulation and traversal techniques. This foundational knowledge prepares them for more advanced studies in complex graph algorithms, data analysis, and network-related tasks.

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