Graph Theory
SEM III BCA 215 (B)
Authors:
ISBN:
Rs.60.00
- DESCRIPTION
- INDEX
‘Graph Theory’ is a Simple version for S.Y.B.C.A. (NEP) students
of our Prashant Publication.
This text is in accordance with the new syllabus NEP-2025
recommended by the Kavayitri Bahainabai Chaudhari North Maharashtra
University, Jalgaon, which has been serving the need of S.Y.B.C.A.
Computer Science students from various colleges. This text is also
useful for the student of Engineering, B.Sc. (Information Technology
and Computer Science), M.Sc, M.C.A., B.B.M., M.B.M. other different
Computer courses.
We are extremely grateful to Prof. Dr. S.R. Kolhe, Chairman, Board
of Studies, and all BOS members of Kavayitri Bahinabai Chaudhari North
Maharashtra University, Jalgaon for his valuable guidance.
We are grateful to Prof.Sanjay E. Pate of Nanasaheb Yashwantrao
Narayanrao Chavan Arts, Science, and Commerce College, Chalisgaon for
coordinating all authors and publication team.
We are obligated to Principals and Librarians and staff of respective
colleges for their encouragement.
We are zery much thankful to Shri. Rangrao Patil of Prashant
Publications, who has shown extreme co-operation during the preparation
of this book, for getting the book published in time and providing an
opportunity to be a part of this book.
We shall be glad to receive any suggestions for improving the contents
of this book.
CHAPTER – 1……………………………………………………………………………………..7
Introduction to Graph Theory
1.1 Definition of a graph and Basic terminology: edge, vertex, graph, degree of vertex, path, cycle
1.2 Types of graphs: Directed, undirected, weighted, mixed graph.
1.3 Operation on graph: Union, Intersection, Join, Cartesian Product, Complement.
1.4 Representation of Graphs: Adjacency Matrix, Adjacency List, Incidence Matrix.
1.5 Application of graph
CHAPTER – 2……………………………………………………………………………………26
Graph Connectivity and Travers ability
2.1 Connectivity
• Connected components
• Cut vertices and cut edges
• Blocks
2.2 Traversability
• Eulerian paths and circuits
• Hamiltonian paths and circuits
CHAPTER – 3……………………………………………………………………………………38
Graph Algorithm
3.1 Shortest Path Algorithms:
• Dijkstra’s Algorithm
• Bellman-Ford Algorithm
3.2 Graph Traversal Techniques:
• Breadth-First Search (BFS)
• Depth-First Search (DFS)
• Floyd-Warshall Algorithm
3.3 Applications in Networking and Database Systems CHAPTER – 4……………………………………………………………………………………52
Trees
4.1 Definition and properties of trees
4.2 Types of trees: Rooted trees, binary trees, spanning trees
4.3 Applications of trees:
• Minimum spanning trees (Prim’s and Kruskal’s algorithms)
• Binary search trees
• Decision trees
• Applications: Applications in computer networks, social networks, and data structures
Author
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