By: Drew Moen. Graph Theory History Leonhard Euler - founder The Seven Bridges of Königsberg Cross every Bridge once Change the city into a graph Change.

Slides:

Advertisements

Similar presentations

CSE 211 Discrete Mathematics

Advertisements

22C:19 Discrete Math Graphs Fall 2010 Sukumar Ghosh.

Introduction to Graph Theory Instructor: Dr. Chaudhary Department of Computer Science Millersville University Reading Assignment Chapter 1.

Chapter 7 Graph Theory 7.1 Modeling with graphs and finding Euler circuits. Learning Objectives: Know how to use graphs as models and how to determine.

Graph Theory: Euler Circuits Christina Mende Math 480 April 15, 2013.

Lecture 21 Paths and Circuits CSCI – 1900 Mathematics for Computer Science Fall 2014 Bill Pine.

Section 14.1 Intro to Graph Theory. Beginnings of Graph Theory Euler’s Konigsberg Bridge Problem (18 th c.)  Can one walk through town and cross all.

AMDM UNIT 7: Networks and Graphs

BY: MIKE BASHAM, Math in Scheduling. The Bridges of Konigsberg.

Management Science 461 Lecture 2b – Shortest Paths September 16, 2008.

The Seven Bridges Of Konigsberg.

Koenigsberg bridge problem It is the Pregel River divided Koenigsberg into four distinct sections. Seven bridges connected the four portions of Koenigsberg.

Graph Theory. What is Graph Theory? This is the study of structures called ‘graphs’. These graphs are simply a collection of points called ‘vertices’

IEOR266 © Classification of MCNF problems.

Introduction to Networks HON207. Graph Theory In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to.

Graphs. Graph A “graph” is a collection of “nodes” that are connected to each other Graph Theory: This novel way of solving problems was invented by a.

Euler and Hamilton Paths

Graph Theory and Graph Coloring Lindsay Mullen

Discrete Math Round, Round, Get Around… I Get Around Mathematics of Getting Around.

The Bridge Obsession Problem By Vamshi Krishna Vedam.

Eulerian Circuits. A Warm Up Problem Jenny & John were at a Math Circles event with three other couples. As people arrived, various handshakes took place.

Can you find a way to cross every bridge only once?

Take a Tour with Euler Elementary Graph Theory – Euler Circuits and Hamiltonian Circuits Amro Mosaad – Middlesex County Academy.

Chapter 15 Graph Theory © 2008 Pearson Addison-Wesley.

1 Starter of the day 23 x 27 = x 47 = x 87 = x 55 = x 58 = ???? 54 x 56 = ???? Can you spot the trick for this group of.

© Nuffield Foundation 2011 Nuffield Free-Standing Mathematics Activity Chinese postman problems What route can I take to avoid going along the same street.

“Graph theory” for the master degree program “Geographic Information Systems” Yulia Burkatovskaya Department of Computer Engineering Associate professor.

Euler and Hamilton Paths

Structures 7 Decision Maths: Graph Theory, Networks and Algorithms.

Euler and Hamilton Paths. Euler Paths and Circuits The Seven bridges of Königsberg a b c d A B C D.

Connected Components Fun with graphs, searching, and queues.

5.4 Graph Models (part I – simple graphs). Graph is the tool for describing real-life situation. The process of using mathematical concept to solve real-life.

L – Modelling and Simulating Social Systems with MATLAB Lesson 6 – Graphs (Networks) Anders Johansson and Wenjian Yu (with S. Lozano.

Lecture 14: Graph Theory I Discrete Mathematical Structures: Theory and Applications.

Konigsburg Bridge Problem The Konigsberg Bridge problem is a famous mathematical problem studied by many students in geometry.

One day a guy approached us with a puzzle he has been pondering on for approximately seven years. He called this the ‘Walls and Lines Puzzle’.

Aim: What is an Euler Path and Circuit?

1.5 Graph Theory. Graph Theory The Branch of mathematics in which graphs and networks are used to solve problems.

Discrete Mathematical Structures: Theory and Applications

CIRCUITS, PATHS, AND SCHEDULES Euler and Königsberg.

Euler Paths and Circuits. The original problem A resident of Konigsberg wrote to Leonard Euler saying that a popular pastime for couples was to try.

MAT 2720 Discrete Mathematics Section 8.2 Paths and Cycles

The Seven Bridges of Konigsberg (circa 1735) In Konigsberg, Germany, a river ran through the city such that in its centre was an island, and after passing.

Lecture 11: 9.4 Connectivity Paths in Undirected & Directed Graphs Graph Isomorphisms Counting Paths between Vertices 9.5 Euler and Hamilton Paths Euler.

Chapter 6: Graphs 6.1 Euler Circuits

Chapter 5: The Mathematics of Getting Around

Review Euler Graph Theory: DEFINITION: A NETWORK IS A FIGURE MADE UP OF POINTS (VERTICES) CONNECTED BY NON-INTERSECTING CURVES (ARCS). DEFINITION: A VERTEX.

M Clements Formal Network Theory. Introduction Practical problem – The Seven Bridges of Königsberg Network graphs Nodes & edges Degrees Rules/ axioms.

Euler and Hamiltonian Graphs

Chapter 14 Section 3 - Slide 1 Copyright © 2009 Pearson Education, Inc. AND.

STARTER: CAN YOU FIND A WAY OF CROSSING ALL THE BRIDGES EXACTLY ONCE? Here’s what this question would look like drawn as a graph.

By Harish Bhattarai, Cameron Halvey, Layton Miller

Graph theory. Graph theory Leonard Euler (“Oiler”)

Konigsberg’s Seven Bridges

Discrete Structures – CNS2300

Color These Maps with Four Colors

MAT 311 Education for Service-- tutorialrank.com

Discrete Maths 9. Graphs Objective

Discrete Math: Hamilton Circuits

This unit is all about Puzzles Games Strategy.

Introduction to Graph Theory Euler and Hamilton Paths and Circuits

Lecture 15: Graph Theory II

Genome Assembly.

Graph Theory By Amy C. and John M..

Konigsberg- in days past.

Graph Theory What is a graph?.

Discrete Mathematics Lecture 13_14: Graph Theory and Tree

Euler and Hamilton Paths

Graph Theory Relations, graphs

Presentation transcript:

By: Drew Moen

Graph Theory History Leonhard Euler - founder The Seven Bridges of Königsberg Cross every Bridge once Change the city into a graph Change the graph into a matrix

Applications Programming Engineering Communications Circuitry Social Networks Shortest Path

Knight’s Tour Hamilton Path A path that visits every vertex on a graph one time Knight’s Tour A path that a knight takes on a n x n or n x m checkerboard to visit every vertex once Setup Create a graph Model graph with a matrix

Purpose Finding new ways to solve for a knight’s tour Figuring out where a knight can arrive with a restricted amount of moves Finding out how many moves a knight needs to get anywhere on the board

Graph

Matrix Three by Three C=[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] Four by Four B=[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]

Matrix Application A 2 =All locations a knight can travel in two moves A 3 = three moves, A 4, A 5, A 6 … C 2 = [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]

More Moves C 3 = [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] C 4 = [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] C 5 = [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]

Patterns [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] C 11 = C 10 =

Work’s Cited Rosen, Kenneth H.. Discrete Mathematics and Its Applications. Fifth. New York, NY: McGraw-Hill, Strang, Gilbert. Introduction to Linear Algebra. Third. Wellesley MA: Wellesley-Cambridge Press, Houry, J K.. "Application to Graph theory." 11 Nov Ramas, Amy. "Art of Knight Graph." knight_tour. 04 July Dec "Graph Theory & Knight's Tour." 18 Dec Farmer, Jesse. "Graph Theory." 31 July Dec Hickethier, Don. Q&A interview. 17 Dec 2008.