CSE 321 Discrete Structures

Slides:



Advertisements
Similar presentations
Simple Graph Warmup. Cycles in Simple Graphs A cycle in a simple graph is a sequence of vertices v 0, …, v n for some n>0, where v 0, ….v n-1 are distinct,
Advertisements

22C:19 Discrete Math Graphs Fall 2010 Sukumar Ghosh.
22C:19 Discrete Math Graphs Fall 2014 Sukumar Ghosh.
Discrete Structures Chapter 7A Graphs Nurul Amelina Nasharuddin Multimedia Department.
CSE 321 Discrete Structures Winter 2008 Lecture 25 Graph Theory.
W. D. Grover TRLabs & University of Alberta © Wayne D. Grover 2002, 2003 Graph theory and routing (initial background) E E Lecture 4.
Chapter 11 Graphs and Trees This handout: Terminology of Graphs Eulerian Cycles.
22C:19 Discrete Math Graphs Spring 2014 Sukumar Ghosh.
GRAPH Learning Outcomes Students should be able to:
Information Networks Introduction to networks Lecture 1.
Can you connect the dots as shown without taking your pen off the page or drawing the same line twice.
Lecture 10: Graphs Graph Terminology Special Types of Graphs
© by Kenneth H. Rosen, Discrete Mathematics & its Applications, Sixth Edition, Mc Graw-Hill, 2007 Chapter 9 (Part 2): Graphs  Graph Terminology (9.2)
 What is a graph? What is a graph?  Directed vs. undirected graphs Directed vs. undirected graphs  Trees vs graphs Trees vs graphs  Terminology: Degree.
1 CS104 : Discrete Structures Chapter V Graph Theory.
1 12/2/2015 MATH 224 – Discrete Mathematics Formally a graph is just a collection of unordered or ordered pairs, where for example, if {a,b} G if a, b.
Graphs and Isomorphisms Discrete Structures (CS 173) Madhusudan Parthasarathy, University of Illinois Backyards of Old Houses in Antwerp in the Snow Van.
Graphs Edge(arc) Vertices can be even or odd or undirected (two-way) Edges can be directed (one-way) This graph is connected. Degree(order) = 3 Odd vertex.
Introduction to Graph Theory
Graph theory and networks. Basic definitions  A graph consists of points called vertices (or nodes) and lines called edges (or arcs). Each edge joins.
Graphs Upon completion you will be able to:
CSE 421 Algorithms Richard Anderson Winter 2009 Lecture 5.
Welcome! Cinda Heeren Lecturer Department of CS UIUC The Beauty of Computer Science.
رياضيات متقطعة لعلوم الحاسب MATH 226. Chapter 10.
Graph Coloring Lots of application – be it mapping routes, coloring graphs, building redundant systems, mapping genes, looking at traffic patterns (see.
Chapter 9 (Part 2): Graphs
Graphs Rosen, Chapter 8.
Lecture 5.2: Special Graphs and Matrix Representation
Lecture 19: CONNECTIVITY Sections
Applied Discrete Mathematics Week 13: Graphs
Copyright © Zeph Grunschlag,
Graph Graphs and graph theory can be used to model:
COT 3100, Spring 2001 Applications of Discrete Structures
ME 123 Computer Applications I Lecture 32: More Simulations 5/9/03
CS 250, Discrete Structures, Fall 2015
Agenda Lecture Content: Introduction to Graph Path and Cycle
Taibah University College of Computer Science & Engineering Course Title: Discrete Mathematics Code: CS 103 Chapter 10 Graphs Slides are adopted from “Discrete.
Graphs and Graph Models
Introduction (with applications) ADT & terminology
Chapter 13 (Part 1): Graphs
Discrete Mathematics and its Applications Lecture 1 – Graph Theory
CS100: Discrete structures
CSE 321 Discrete Structures
Week of March th grade.
Graph Theory By Amy C. and John M..
Graphs Discrete Structure CS203.
Graphs.
August 2018 Monday Tuesday Wednesday Thursday Friday
CSE 373 Data Structures Lecture 17
Course calendar (page 1 of 2)
CSE 321 Discrete Structures
Richard Anderson Lecture 26 NP-Completeness
Discrete Mathematics Lecture 13_14: Graph Theory and Tree
Let us switch to a new topic:
Richard Anderson Winter 2009 Lecture 6
CSE 321 Discrete Structures
Lecture 10: Graphs Graph Terminology Special Types of Graphs
Graphs G = (V, E) V are the vertices; E are the edges.
Miniconference on the Mathematics of Computation
GRAPHS G=<V,E> Adjacent vertices Undirected graph
CSE 321 Discrete Structures
Chapter 10 Graphs and Trees
HW 3 (Due Wednesday Feb 6) Create slide(s) for your 1 minute presentation on a graph theory application. Make sure your slide(s) include (1) Define the.
Richard Anderson Winter 2019 Lecture 6
Richard Anderson Winter 2019 Lecture 5
CSE 321 Discrete Structures
HW 3 (Due Wednesday Feb 6) Create slide(s) for your 1 minute presentation on a graph theory application. Make sure your slide(s) include (1) Define the.
CSE 321 Discrete Structures
CSE 373 Data Structures Lecture 13
For Friday Read chapter 9, sections 2-3 No homework
Presentation transcript:

CSE 321 Discrete Structures Winter 2008 Lecture 25 Graph Theory

Announcements Readings Schedule This week Lecture Monday, Wednesday Graph Theory, 9.1 – 9.4 Schedule Lecture Monday, Wednesday Quiz Section, Thursday No class Friday. Review Session, TBA Final Exam, Monday, March 17

Highlights from Lecture 24 Composition by Matrix Multiplication Equivalence Relations Ordering relations Total Order Partial Order

Ordering examples Total Orders Partial Orders Lexicographic Order Prerequisites Dominance order

Graph Theory Graph formalism Directed Graph Undirected Graph G = (V, E) Vertices Edges Directed Graph Edges ordered pairs Undirected Graph Edges sets of size two

Graph examples Communication Networks Road networks

Social networks Community Graph Transactions Authorship Linked In, Face Book Transactions Ebay Authorship Erdos Number

The web graph

Page Rank Determine the value of a page based on link analysis Model of randomly traversing a graph Weighting factors on nodes Damping (random transitions)

Graph terminology Neighborhood Degree

Degree sequence Find a graph with degree sequence 3, 3, 2, 1, 1 3, 3, 3, 3, 3

Handshake Theorem

Directed Degree Theorem

Special Graphs Complete Graphs Kn Cycle Cn Hypercube Qn Mesh Mn,m

Bipartite Graphs