B.E. (Computer Engineering) Discrete Structures and Graph Theory Syllabus - Mumbai University 2026

The University has moved this degree onto NEP 2020 one year at a time. The first and second years are NEP 2020 syllabi; the third and fourth years are still examined on the REV-2019 'C' Scheme, which is what the University sets for them this year.

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Syllabus for Discrete Structures and Graph Theory

Semester 3 · Second Year CE · 3 credits · 100 marks

Module 0: Prerequisite

Basic Set Theory, Logical Operators, Truth Tables, Cartesian product, Types of Functions. Basic Algebra and Number Theory, Fundamental Counting Principle, Permutations, Combinations. Graph Basics.

Module I

Set Theory: Sets, Subsets, Universal and Empty Sets, Set Operations, Set Representation, Laws of Set theory. Logic: Propositional Logic, Predicate Logic, Quantifiers (Universal and Existential). Types of Mathematical Proof: Direct proof, Proof by contradiction, Proof by deduction, Proof by cases, Proof by exhaustion, Proof by counterexample, Mathematical induction. Self-learning Topics: PROLOG / LISP programming to create expert system using Propositional and Predicate Logic, Other types of logic and sets. Relations: Definition, Representation of Relations, Properties of Relations, Equivalence Relations, Equivalence Classes, Closures of Relations, Warshall’s algorithm. Posets and Lattice: Partial Order Relations, Poset, Hasse Diagram, Chain and Anti chains, Lattice, Types of Lattices, Sub lattice. Self-learning Topics: Practical applications of relations in real life in the field of Database Management, Economics, Social Network, Sports, Medical Diagnosis, Weather, etc. Functions: Types: Injective, Surjective, and Bijective Functions. Composition, Inverse Functions. Real life applications of Functions. Self-learning Topics: Practical applications of function in Neural Network, Determining risk factors for insurance rates, Taxes and tax brackets, Vending machines, etc. Pigeonhole Principle, Inclusion-Exclusion Principle. Recurrence relations, Solving recurrence relations Self-learning Topics: Applications of Recurrence Relations – Analysis of recursive algorithms in computing. Combinatorial Problem Solving Using counting techniques in probability and decision-making. Algebraic structures with one binary operation: Semi group, Monoid, Groups, Subgroups, Abelian Group, and Cyclic group. Algebraic structures with two binary operations: Ring. Self-learning Topics: Error Correcting codes.

Module VI: Graph Theory

Types of graphs, Graph Representation, Sub graphs, Operations on Graphs, Walk, Path, Circuit, Connected Graphs, Disconnected Graph, Components, Homomorphism and Isomorphism of Graphs, Euler and Hamiltonian Graphs, Planar Graph, Cut Set, Cut Vertex, Real life applications of Graph Theory. Self-learning Topics: Network Flow Problems Understanding flow in networks and its optimization. Graph Coloring Applications in Scheduling – Use of graph coloring in timetabling and resource allocation. Optimization Techniques Application of graphs in shortest path problems, spanning trees, and clustering.

Text Books

1 Susanna S. Epp, “Discrete Mathematics with Applications”, 5th Edition, Cengage Publications.
2 Ralph P. Grimaldi, “Discrete and Combinatorial Mathematics”, 5th Edition, Pearson Publications.
3 Edgar Goodaire and Michael Parmenter, “Discrete Mathematics and Graph Theory”, 3 rd Edition, Pearson Publications.
1 Kenneth A. Ross, “Discrete Mathematics”, 5 th Edition, Pearson Publications.
2 Swapan Kumar Sarkar, “Textbook of Discrete Mathematics”, 9 th Edition, S. Chand Publications.
3 Bernad Kolman, Robert Busby, Sharon Cutler Ross, Nadeem-ur-Rehman, “Discrete Mathematical Structures”, 6th Edition, Pearson Education.
4 T. Veera Rajan, “Discrete mathematics with Graph Theory and Combinatorics”, McGraw Hill Publications.
5 C. L. Liu “Elements of Discrete Mathematics”, second edition 1985, McGraw-Hill Book Company. Reprinted 2000

Reproduced from the University of Mumbai syllabus for B.E. (Computer Engineering) under NEP 2020, in force from the academic year 2025-26. Wording is as printed in that syllabus. Module numbering is as printed there too.

The complete syllabus

This subject is cut from the University circular for its year. Open a document here if you want the whole thing rather than a single subject.

PDF 7.9 (R-A) B.E. (Computer Engineering) Sem I & II (Revised, NEP 2020) NEP 2020 syllabus Read full PDF Read

PDF 6.24 (N) B.E. (Computer Engineering) Sem III & IV (NEP 2020) NEP 2020 syllabus Read full PDF Read

PDF 6.15 B.E. (Computer Engineering) Third Year, Sem V & VI (REV-2019 'C' Scheme) REV-2019 'C' Scheme syllabus Read full PDF Read

PDF 6.41 (R) B.E. (Computer Engineering) Fourth Year, Sem VII & VIII (REV-2019 'C' Scheme) REV-2019 'C' Scheme syllabus Read full PDF Read

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