Discrete Mathematics and Graph Theory Reading Notes Common to CSE, IT, CSE( DS), CSE (IoT), CSE

(AI), CSE (AI & ML) and the AI & DS branches

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

## Discrete mathematics and graph theory 2 years BTech 3 semesters Syllabus

### UNIT – I Mathematical Logic

Introduction, statements and notation, connectives, well-formed formulas, tautology, law of duality, equivalence, implication, normal forms, set of functionally complete connectives, statement calculus inference theory, predicate calculus, inference theory of predicate calculus.

### UNIT – II Set Theory

Basic concepts of set theory, relations and ordering, inclusion-exclusion principle, dovecote principle and its application, composition of functions of functions, inverse functions, recursive functions, lattices and their properties.

Algebraic structures: algebraic systems – examples and general properties, semigroups and monoids, groups, subgroups, homomorphism and isomorphism.

### UNIT – III Elementary Combinatorics

Basics of counting, combinations and permutations, enumeration of combinations and permutations, enumeration of combinations and permutations with repetitions, enumeration of permutations with constrained repetitions, binomial coefficients, binomial and multinomial theorems.

### UNIT – IV Recurrence Relations

Sequence generating functions, calculation of coefficients of generating functions, recurrence relations, resolution of recurrence relations by substitution and generating functions, method of characteristic roots, solutions of inhomogeneous recurrence relations.

### UNIT – V Charts

Basic concepts, isomorphism and subgraphs, trees and their properties, spanning trees, directed trees, binary trees, planar graphs, Euler’s formula, multigraphs and Euler’s circuits, Hamiltonian graphs, chromatic numbers, four color problem.

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