CENG 110 • Final • Discrete Structures

Definition of Relation

Example 1

Example 2

Example 3

Example 4

Reflexive Relations

Example 5

Example 6

Symmetric Relations

Antisymmetric Relations

Example 7

Transitive Relations

Example 8

Properties of Relations

Example 9

Example 10

Example 11

Example 12

Equivalence Relation

Example 13

Example 14

Example 15

Partially Ordered Set

Example 1

Example 2

Example 3

Totally Ordered Set

Example 4

Hasse Diagram

Example 5

Maximal and Minimal Elements

Greatest and Least Elements

Example 6

Upper and Lower Bound

Least Upper and Greatest Lower Bound

Example

Relations 1

Relations 2

Relations 3

Relations 4

Relations 5

Relations 6

Relations 7

Relations 8

Relations 9

Relations 10

Introduction

Graph Terminology

Handshaking Theorem

Example 1

Special Graphs

Example 2

Bipartite Graphs

Example 3

Example 4

Complete Bipartite Graph

Matching

Subgraph

Example 5

Subgraph Induced

Edge Contraction

Example 6

Complementary Graph

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

Adjacency Matrices

Incidence Matrices

Bipartite Graphs & Euler Circuits

Euler Path, Induced Subgraph & Incidence Matrix

Isomorphism 1

Isomorphism 2

Isomorphism 3

Isomorphism 4

Isomorphism 5

What is a network?

Shortest Path Problems

Dijkstra's Algorithm

Djikstra's Algorithm Example 1

Djikstra's Algorithm Example 2

Shortest Path Problem Example 1

Shortest Path Problem Example 2

Problem Definition

Solving Problem

Enumeration

Example 1

Nearest Neighbor Algorithm

Example 2

Example 3

Djikstra's Algorithm

Shortest Path Problem 1

Shortest Path Problems 2

Shortest Path Problems 3

Shortest Path Problems True/False 1

Shortest Path Problems True/False 2

Traveling Salesperson Problem 1

Traveling Salesperson Problem 2

Traveling Salesperson Problem 3