CMPE 251 • Final • Discrete Computational Structures

Introduction

Proof of Formulas by Induction

Example 1

Example 2

Example 3

Example 4

Proof of Divisibility by Induction

Example 1

Example 2

Proof of Inequality by Induction

Example 1

Example 2

Induction Related to Fibonacci

Strong Induction

Induction for Formulas 1

Induction for Formulas 2

Induction Proof for Divisibility 1

Induction Proof for Divisibility 2

Induction for Inequalities 1

Induction for Inequalities 2

Induction for Inequalities 3

Induction for Inequalities 4

Induction with Fibonacci 1

Induction with Fibonacci 2

Induction with Fibonacci 3

Induction with Fibonacci 4

Strong Induction 1

Strong Induction 2

Introduction

Example 1

Graph Terminology

Example 2

Handshaking Theorem

Example 3

Example 4

Special Graphs

Example 5

Example 6

Bipartite Graphs

Example 7

Example 8

Complete Bipartite Graph

Matching

Example 9

Subgraph

Example 10

Subgraph Induced

Edge Contraction

Example 11

Complementary Graph

Example 12

Example 13

Example 14

Adjacency Matrices - Undirected Graphs

Adjacency Matrices - Directed Graphs

Example 1

Example 2

Incidence Matrices

Example 3

Isomorphism of Graphs

Example 4

Example 5

Example 6

Example 7

Definition of Paths and Circuits

Connected Graphs

Euler Paths and Circuits

Example 8

Hamilton Paths and Circuits

Example 9

Example 10

Graphs 1

Graphs 2

Graphs 3

Graphs 4

Graphs 5

Graphs 6

Graphs 7

Graphs 8

Graphs 9

Graphs 10

Graphs 11

Graphs 12

Graphs 13

Graphs 14

Graphs 15

Graphs 16