Discrete Mathematics & Graph theory Lecture Notes Common to CSE, IT, CSE( DS), CSE (IoT), CSE

(AI), CSE (AI & ML) and AI & DS Branches

All below syllabus is coved in this lecture note Discrete Mathematics and Graph Theory PDF copy.

## Discrete Mathematics & Graph Theory 2-year BTech 3-semester Syllabus

### UNIT – I Mathematical Logic

Introduction, Statements, and Notation, Connectives, Well-formed formulas, Tautology, Duality law, Equivalence, Implication, Normal Forms, Functionally complete set of connectives, Inference Theory of Statement Calculus, Predicate Calculus, Inference theory of Predicate Calculus.

### UNIT – II Set theory

Basic Concepts of Set Theory, Relations and Ordering, The Principle of InclusionExclusion, Pigeon hole principle and its application, Functions composition of functions, Inverse Functions, Recursive Functions, Lattices, and its properties.

Algebraic structures: Algebraic systems-Examples and General Properties, Semi groups and Monoids, groups, subgroups, homomorphism, and Isomorphism.

### UNIT – III Elementary Combinatorics

Basics of Counting, Combinations, and Permutations, Enumeration of Combinations and Permutations, Enumerating Combinations and Permutations with Repetitions, Enumerating Permutations with Constrained Repetitions, Binomial Coefficients, The Binomial and Multinomial Theorems.

### UNIT – IV Recurrence Relations

Generating Functions of Sequences, Calculating Coefficients of Generating Functions, Recurrence relations, Solving Recurrence Relations by Substitution and Generating functions, The Method of Characteristic roots, Solutions of Inhomogeneous Recurrence Relations.

### UNIT – V Graphs

Basic Concepts, Isomorphism and Subgraphs, Trees and their Properties, Spanning Trees, Directed Trees, Binary Trees, Planar Graphs, Euler’s Formula, Multigraphs, and Euler Circuits, Hamiltonian Graphs, chromatic Numbers, The Four Color Problem.

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