Graph Theory BCS405B
Module-wise notes, PYQs, and a built-in resource explorer — everything you need to crack BCS405B in one focused page.
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Module 1 Overview
Introduction to Graphs: Introduction- Basic definition - Application of graphs - finite, infinite and bipartite graphs - Incidence and Degree - Isolated vertex, pendant vertex and Null graph. Paths and circuits - Isomorphism, sub-graphs, walks, paths and circuits, connected graphs, disconnected graphs and components.
(RBT Levels: L1, L2 and L3)
Teaching-Learning Process: Chalk and talk method / PowerPoint Presentation
Module 2 Overview
Eulerian and Hamiltonian graphs: Euler graphs, Operations on graphs, Hamiltonian paths and circuits, Travelling salesman problem. Directed graphs - types of digraphs, Digraphs and binary relation.
(RBT Levels: L1, L2 and L3)
Teaching-Learning Process: Chalk and talk method / PowerPoint Presentation
Module 3 Overview
Trees: properties, pendant vertex, Distance and centres in a tree - Rooted and binary trees, counting trees, spanning trees.
Connectivity Graphs: Vertex Connectivity, Edge Connectivity, Cut set and Cut Vertices, Fundamental circuits.
(RBT Levels: L1, L2 and L3)
Teaching-Learning Process: Chalk and talk method / PowerPoint Presentation
Module 4 Overview
Planar Graphs: Planar graphs, Kuratowski's theorem (proof not required), Different representations of planar graphs, Euler's theorem, Geometric dual.
Graph Representations: Matrix representation of graphs-Adjacency matrix, Incidence Matrix, Circuit Matrix, Path Matrix.
(RBT Levels: L1, L2 and L3)
Teaching-Learning Process: Chalk and talk method / PowerPoint Presentation
Module 5 Overview
Graph Colouring: Colouring- Chromatic number, Chromatic polynomial, Matchings, Coverings, Four colour problem and Five colour problem. Greedy colouring algorithm.
(RBT Levels: L1, L2 and L3)
Teaching-Learning Process: Chalk and talk method / PowerPoint Presentation
Resource Explorer
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Frequently Asked Questions
What is BCS405B (Graph Theory BCS405B)?
Graph Theory BCS405B is a VTU course covered through module-wise syllabus, notes, and PYQ-driven exam practice available on this page.
How many credits is BCS405B?
Credits for BCS405B: 03.
Are notes and previous year question papers available for BCS405B?
Yes. You can access organized notes, PDFs, and PYQ material from the file explorer/resources section on this page.
How should I prepare Graph Theory BCS405B for VTU exams?
Start with module summaries, solve recent PYQs unit-wise, and finish with complete paper practice under time constraints for SEE readiness.
Is this BCS405B page updated for current VTU scheme?
Yes, this page is maintained with current scheme-oriented materials and practical exam-focused resource curation.
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About Graph Theory (BCS405B)
Graph Theory (BCS405B) is a critical course in the VTU curriculum, essential for any student looking to master the foundations of engineering. It covers key theoretical frameworks and practical concepts that are widely used in the industry today, ensuring students are well-prepared for both exams and their future careers.
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