Documents about Graph Theory
h11
Washington, M 381
Excerpt: ... Math 381 Handout 11 R. J. LeVeque October 26, 1998 Midterm Review The midterm exam is scheduled for next Monday, November 2. You may bring one page of hand-written notes both sides to the exam if you wish. The exam will cover basic techniques that we have studied and seen on the homework. In particular: Combinatorics and counting arguments Sum rule, product rule, permutations, number of subsets, etc. Estimating complexity of an algorithm Graph theory and network algorithms: Setting up a simple model as a graph theory problem Dijkstra's algorithm for shortest path Algorithms for nding minimum spanning trees Linear programming: Formulating problems as linear programs, e.g., mixing problems Graphical solution of problems with 2 variables and several constraints Feasible set, level sets of objective function Matrix iteration methods and Markov chains will not be on the exam. 1 ...
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lecture14
George Mason, MATH 6390
Excerpt: ... Bioinformatics Lecture Notes Announcements Class 14 February 19, 2002 1. Evolutionary Problems i) Markov Processes (text p 140-144) Finish determination of substitution matrix for nucleotides. ii) Clustering Methods How do we determine the best fit phylogenetic data? Cannot determine the minimum number of mutations for all possible tree topologies having n leaves since the number of binary trees is exponential. Instead we will use some concepts from graph theory a) ultrameric trees b) additive metric c) estimating branch lengths ...
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lec2
University of Illinois, Urbana Champaign, CS 473
Excerpt: ... Basic Graph Theory Breadth First search Depth First Search Directed Graphs CS 473ug: Algorithms Mahesh Viswanathan vmahesh@cs.uiuc.edu 3232 Siebel Center University of Illinois, Urbana-Champaign Spring 2008 Viswanathan CS473ug Basic Graph Theory Breadth First search Depth First Search Directed Graphs Graphs Connectivity in Graphs Trees Graph Representation Transportation Networks Albany Chicago New York Champaign Miami Scheme Points denote cities, warehouses, ports, airelds, etc. A line between x and y denotes the ability to move goods, people, etc. from x to y . Goal Design network so that trac can move eciently, reliably . . . Viswanathan CS473ug Basic Graph Theory Breadth First search Depth First Search Directed Graphs Graphs Connectivity in Graphs Trees Graph Representation Social Networks 5 7 1 1. Canopy: leaves, fruit, owers 2. Canopy animals: bird, fruitbats, and other mammals 3. Upper air mammals: birds and bats 4. Insects 5. Large ground animals: large mammals 6. Trunk, fru ...
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370syl
Cal Poly Pomona, WEB 370
Excerpt: ... MAT 370-01 Graph Theory TuTh 3:00pm-4:50pm 8-156 Instructor: Brent Deschamp Email: bjdeschamp@csupomona.edu Website: http:/www.csupomona.edu/bjdeschamp Oce: 8-154 Phone: 909-869-3485 Oce Hours: Monday Tuesday 2-3pm Wednesday 9-10am, 3-5pm Thursday 2-3pm And by appointment Recommended Text: Introduction to Graph Theory by Douglas B. West, Second Edition The only resources available to you for this course are your notes and this book. Course Description: The study of graphs, trees, Eulerian, Hamiltonian, planar graphs, connectivity, coloring, independence and covering numbers, directed graphs, theorems of Menger, Ramsey with applications. 4 lecture/problemsolving. Grading: Quizzes Homework 10% 20% Project 1 Project 2 15% 15% Exam 1 Exam 2 20% 20% A grade of at least a C is required on both projects for successful completion of this course. Quizzes: Quizzes will be given over denitions and the statement of important theorems on a regular and unannounced basis. Homework: Problem sets will be distr ...
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exinfo
Wisconsin, ECE 556
Excerpt: ... ECE 556 Design Automation of Digital Systems Midterm Examination Information Date: October 14, 2004 Time: 1:00 - 2:15 PM Location: Class room Rules: a. Closed book examination b. one single-side, letter-size "fact sheet" is allowed during exam. Coverage: Combinatorial algorithms, bin-packing problem (Appendix A, lecture notes) Graph theory , shortest path algorithm (lecture notes) Circuit paritioning: Kernighan-Lin, Fiduccia Mattheyses, Simulated Annealing (Section 2.1-2.4) Floor planning, slicing structure, Polish expression, bounding curve, Simulated annealing, mathematical programming method (Section 3.1-3.2, 3.3.2, 3.3.3) ...
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335
Cal Poly, MATH 335
Excerpt: ... September 2008 MATH 335 Graph Theory 1. Catalog Description MATH 335 Graph Theory (4) Introduction to graph theory and its applications: isomorphism, paths and searching, connectedness, trees, tournaments, planarity, graph colorings, matching theory, network flow, adjacency and incidence matrices. Further topics to be selected from the theory of finite state machines, Ramsey theory, extremal theory, and graphical enumeration. 4 lectures. Prerequisite: Junior standing or consent of instructor. 2. Required Background or Experience Junior standing. 3. Learning Objectives The student should gain an understanding of the fundamental concepts of graph theory . 4. Text and References Possible texts: Buckley, Fred and Marty Lewinter, A Friendly Introduction to Graph Theory , Prentice-Hall, 2002. Chartrand, G. and Linda Lesniak, Graphs and Digraphs, 4th ed., Chapman & Hall/CRC, 2004. West, Douglas B., Introduction to Graph Theory , 2nd ed., Prentice-Hall, 2000. Wilson, Robin J., Introduction to Graph Theory , 4th ed., Add ...
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hwk8
UMass (Amherst), CS 591
Excerpt: ... Computer Science / Mathematics 591J Combinatorics and Graph Theory Homework Assignment 8 Due Date: in class - 4-15 (Thursday) These problems are from section 6.2 1. 4 2. 6 3. 14 4. 24 5. 26 Also: 6. #14, page 264 Note: you may collaborate with another person on these - just say who, and which problems. You MUST do at least 3 completely on your own. ...
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references
Clemson, CPSC 940
Excerpt: ... References Graphs & Digraphs, G. Chartrand and L. Lesniak Graph Theory , R. Diestel Graphs on Surfaces, B. Mohar and C. Thomassen Planar Graphs: Theory and Algorithms, T. Nishizeki and N. Chiba Introduction to the Theory of Computation, M. Sipser Algorithm Design (Pie), E. Tardos and J. Kleinberg Graph Theory , D. West wikipedia.org 1 ...
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G6-review-Guo
Minnesota, HW 8715
Excerpt: ... - Review Form Title of Paper: Representing a River Network based on Graph Theory in PostGIS and visualized with MapServer Authors: Chandana Gangodagamage, David Moretz Reviewer Team (Name, Student Ids): G1, Liang Guo, 2321332 Date Review Completed: April 8, 2006 Comments to Authors (Specific suggestions for improvements): Please see the attachments for details. -Relevance to Databases (check one): very low _ low _ marginal _ high _X_ very high _ Significance of Contribution: very low _ low _ marginal _X_ high _ very high _ Readability and Organization: very poor _ poor _ marginal _ good _X_ very good _ Length (Relative to the useful contents of the paper): too long _ too short _ just right _X_ Fusion of Theory and Practice: inadequate _ marginal _ adequate _X_ - ...
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MATH 240 CO F06
Imperial, MATH 122
Excerpt: ... IMPERIAL COMMUNITY COLLEGE DISTRICT IMPERIAL VALLEY COLLEGE COURSE OUTLINE DIVISION: Science, Mathematics, and Engineering COURSE TITLE: Discrete Mathematics LEC HRS: 3 DATE: September 2006 UNITS: . 3 COURSE NO.: MATH 240 LAB HRS: HRS. TBA: If cross-referenced, please complete the following: COURSE NO.(s): I. . COURSE TITLE: . COURSE/CATALOG DESCRIPTION: This course is an introduction to the theory of discrete mathematics and introduces elementary concepts in logic, set theory, graph theory , number theory and combinatorics. This forms a basis for upper division courses in mathematics and computer science, and is intended for the transfer student planning to major in these disciplines. The topics covered in this course include methods of proof, sets and relations, number theory, induction, recursion, counting principles, permutations, combinations, and graph theory . II. A. PREREQUISITES, IF ANY: MATH 192 with a grade C or better. B. CO-REQUISITES, IF ANY: None C. RECOMMENDED PREPARATION, IF ANY: ...
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820outline
Sveriges lantbruksuniversitet, MATH 820
Excerpt: ... Graduate course announcement Graph Theory Math 820-4 Spring 2004 Luis Goddyn This course will be a foray into several topics in the theory of graphs. The rst half of the course will be a survey of some major branches of this broad eld. The second half will examine specic topics in greater depth. I intend to address both theoretical and algorithmic aspects, which should make the course interesting for computer scientists as well as mathematicians. 11 00 11 00 111 000 11 11 11 11 111 00 00 00 00 000 111 111 000 000 11 00 11 00 Prerequisite: The student should have an undergraduate level of understanding of graph theory , with familiarity with some of the basic notions such as trees, connectivity, paths, cycles, and colourings, and/or associated algorithms. Format: Both depth and breadth of knowledge are vital to this topic. Breadth will be addressed by a series of lectures by myself during January and part of February, Topics will be a subset of the following, and may vary according to student inter ...
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320_01
Virgin Islands, CS 320
Excerpt: ... rk A. Hicks, illustrator. From: Gurl Guide to programming. Jennifer Sean My Research: Large Combinatorial Searches Independent Set: Set of vertices which are pairwise non-adjacent Fullerenes: Working with Patrick Fowler (chemist) Graphite Diamond Topological Graph Theory : Algorithms and Obstructions COMBINATORIAL ALGORITHMS GROUP University of Victoria http:/www.cs.uvic.ca/~wendym/cag Our research interests include: Graph Theory and Graph Algorithms Combinatorics Join our listserv to get information about Combinatorial Algorithms conferences and research talks. Computational Geometry Undergrads are welcome to all events. Randomized Algorithms Computational Complexity Network Reliability Topological Graph Theory Computational Biology Cryptography Design Theory Int. Workshop on Exact and Parameterized Computation, Victoria, May 14-16. 40th ACM Symposium on Theory of Computing, Victoria, May 17-20. CSC 320 Logistics Course Website: http:/www.cs.uvic.ca/~wendym/320.html Instructor: Dr. Wendy Myr ...
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Graph_theory_books
SHSU, MATH 560
Excerpt: ... References for Math 560 Fall 2004 August 27, 2004 Graph Theory Books Introduction to Graph Theory by Douglas B West Introduction to Graph Theory by Robin J Wilson Graphs and Digraphs by Gary Chartrand and Linda Lesniak Knot Theory Books The Knot Book by Colin C Adams Why Knot? by Colin C Adams Knots and Links by Dale Rolfson When Topology Meets Chemistry by Erica Flapan 1 ...
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final_study_F03
Maryland, EE 610
Excerpt: ... File: c:\temp\courses\fall2003\610\final_study_F03.doc RWN 12/14/03 ENEE 610 Fall 2003 Final Exam Study Points - updated (fourth) version (other updates may occur through Monday, 12/15/03) 1. The exam will be open book, open notes (notebooks will be due at the end of the exam). 2. There will be three multipart questions, two based upon the class notes and textbook material and one based upon papers presented. 3. Two questions will be available associated with the papers presented by (everyone will choose one of the questions): a) Keeley b) Jaleel 4. Other topics to study a) Graph theory , semistate and state equations (setting up) and finding vo/vi. b) Properties of passive circuits - positive-real conditions and synthesis. c) Use of gyrators and Spice terminology as well as controlled sources d) Equations for regions of operation of NMOS transistors. e) Indefinite Y matrix and elimination of internal nodes. f) Bridge circuits and their balance. ...
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Exam3_Study_Guide
UMBC, MATH 100
Excerpt: ... Exam 3 Study Guide Math 100, Fall 2008 Terms/Denitions: Be able to dene and use: - All terms dened in FAPP, Chaps 1-4 (see Review Vocabulary at end of each chapter) Graph Theory : Euler Circuits Condition for existence (called "Euler's Theorem" in the book [FAPP, pg 9]) Algorithm for nding (Fleury's Algorithm, [FAPP, pg 10]) Chinese Postman problem (called "Eulerization" and "Squeezing" in the book) Hamilton Circuits Traveling Salesman Problem Planning & Scheduling: Critical Path Method (see Taylor, Chap 20): Finding critical paths, earliest start/end times, latest start/end times, slack Forward and Backward passes Program Crashing - Computing simple problems by hand, and recasting as a linear programming problem PERT Method (see Taylor, Chap 20): Compute expected time and variance/standard deviation for tasks from optimistic, pessimistic and most likely times Linear Programming: Linear Programming: Denitions Simplex Method Solve a simple two variable problem graphically Problems solvable as lin ...
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hwk7
UMass (Amherst), CS 591
Excerpt: ... Computer Science / Mathematics 591J Combinatorics and Graph Theory Homework Assignment 7 Due Date: in class - 4-8 These problems are from section 5.3,5.4,5.5 5.3 1. 2 2. 10 3. 16 4. 18 5. 22 5.4 6. 2 7. 4 8. 20 9. 30 10. 38 11. 40 12. 48 5.5 13. 10 14. 16 15. 26 Note: you may collaborate with another person on these - just say who, and which problems. You MUST do at least 8 completely on your own. ...
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5707hw5
Minnesota, MATH 5707
Excerpt: ... Math 5707 Graph Theory Homework 5, Due Wednesday March 11 Spring 2009 Reading: Chapter 4 Textbook Exercises: 4.2, 4.19, 4.28 Additional Exercises: A1 Consider a nontrivial connected graph G and let H G be a maximal acyclic subgraph. (In this case maximal means no edge can be added without creating a cycle.) Prove that H is a spanning tree for G. [Note: This result proves that Kruskals algorithm actually creates a spanning tree.] ...
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hwk9
UMass (Amherst), CS 591
Excerpt: ... Computer Science / Mathematics 591J Combinatorics and Graph Theory Homework Assignment 9 Due Date: in class - 4-29 (Thursday) These problems are from section 7.1 1. 6 2. 8 3. 18 4. 20 5. 34 Also: section 7.4 6. 6 7. 10 section 7.5 8. 6 9. 8 Note: you may collaborate with another person on these - just say who, and which problems. You MUST do at least 3 completely on your own. ...
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Cycle_graphs
University of the Sciences in Philadelphia, MATH 360
Excerpt: ... Special Topics Course Lia Vas Cycle Graphs of Groups The whole idea here is that sometimes it is better to represent a group graphically that using presentations, listing all the elements or using Cayley tables. This is true especially for groups with larger number of elements when Cayley table become hard to read. So, the idea is to represent a group graphically as a graph. A graph is a set of objects called vertices or nodes some of which are connected by links called edges. So, graph is a set of vertices together with edges between them. Graph are used to represent different objects and the relations between them. The following paragraph on applications of graph is taken from Wikipedia: Many applications of graph theory exist in the form of network analysis. These split broadly into two categories. Firstly, analysis to determine structural properties of a network, such as whether or not it is a scale-free network, or a small-world network. Secondly, analysis to find a measurable quantity within the networ ...
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Modified-Spring-2005-Outline-864
E. Kentucky, EECS 864
Excerpt: ... Course Outline s s s s s Overview of Enabling Technologies-Physical Layer Issues in WDM Networking Wavelength Routed Networks Material from Chapter 2 and Chapter 5 IP over WDM Network Survivability s Optical Control Plane s Link Management Protocol (LMP) MPLS MPS GMLPS Optical Link Layer s s s Same basics of Graph Theory Gigbit and 10 Gigbit Ethernet Digital Wrapper Generic Framing Procedure Some Basics of Mathematical Programming Student Lectures Introduction 1 ...
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XCNetworkSynthesisII-Synthesis
W. Alabama, CHE 720
Excerpt: ... hich uses the heat exchange requirements from the targeting exercise of the previous lecture (HENS 1 - Targeting). This is shown on the following slide. Recall that all heat transfer rates are in gJ/h. 2/24/99 HENS 2 . Synthesis 3 HEAT SOURCES H2 4.410 (4.410) (0.294) H1 2.860 Hot Utility 0.064 (0.696) (0.064) (1.870) C2 4.704 C1 1.870 HEAT SINKS Cold Utility 0.760 The five connecting lines represent five heat exchangers conecting the heat sources to the heat sinks. The number in brackets is the amount of heat to be transferred by that exchanger. EXAMPLE #1: NUMBER OF EXCHANGERS FOR MINIMUM ENERGY CONSUMPTION 2/24/99 HENS 2 . Synthesis 4 INTERPRETATION OF EXAMPLE #1 Example # 1 requires five heat exchangers as shown on the previous slide. Question: Is there any way to determine this without drawing the diagram? Answer: Yes. Graph Theory provides a theorem relating the number of Edges (Heat Exchangers) required to connect a given number of Nodes (Sources and Sinks). This is Nexchangers = Nstrea ...
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dklein
Lake City CC, CS 5400
Excerpt: ... Lottery Design CS-5400 Seminar Daniel M. Klein A lottery is a game in which a person chooses k numbers from a set of n numbers to form a ticket, and where a winning ticket of p numbers is chosen and where the person wins if t or more of the numbers o ...
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acks
Clemson, MATH 419
Excerpt: ... 12 References Finite Mathematics, S.C. Althoen and R.J. Bumcrot, Norton, 1978. An Introduction to Cryptography, Course-notes: University of Natal, G.Barbour, 1998. Fundamentals of Algorithmics, G.Brassard and P.Bratley, Prentice-Hall, 1996. Graphs & Digraph (various editions), G. Chartrand and L. Lesniak. Introduction to Algorithms, T.H.Cormen, C.E.Leiserson, and R.L.Rivest, MIT Press, 1990. A First Course in Abstract Algebra, J.B. Fraleigh, Addison-Wesley, 1982. Pearls in Graph Theory , N. Hartsfield and G. Ringel, Academic Press, 1990. Cryptography: Theory and practice, D.R.Stinson, CRC Press, 1995. Data Structures and Problem Solving in Java (3rd ed), M.A. Weiss, Addison-Wesley, 2005. Introduction to Graph Theory , D. West, Prentice-Hall, 1996. wikipedia.org ...
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BasicGraphTheory
Columbus State University, CPSC 5127
Excerpt: ... Basic Graph Theory Graph theory provides a mathematical structure that is convenient for understanding a number of problems and writing algorithms to solve them. At one level, graphs are very simple. They are just dots connected by lines. The dots, generally drawn as labeled circles, are called vertices (singular is vertex) or nodes. The lines are usually called edges, but may be called links or arcs. The vertices are generally labeled by positive integers, but can be labeled otherwise. In a graph that is read as a map, many of the vertices are labeled with city names. One special class of graphs is called trees, to be defined soon. For some reason, we tend to use the term node when discussing trees and use the term vertex when discussing general graphs. Formal Graph Theory Intuitive graph theory , such as presented above, often suffices for computer science. This lecture will present an introduction to formal graph theory , which is based on set th ...
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Euler
Hobart and William Smith Colleges, MATH 110
Excerpt: ... Math 110: Class 1 Connect the Dots: Graph Theory There's an entire branch of mathematics called graph theory . Mathematicians interested in this subject study graphs. Note: One of the important aspects of mathematics is that each new concept should be carefully defined. So what is a graph? Without being too technical we can define a graph as follows. Definition. A graph is a finite set of of vertices (or points) and edges (segments or arcs) connecting pairs of vertices. A graph is connected if we can travel from one vertex to any other along edges of the graph. Z For simplicity we will, (1) assume that all graphs we discuss today are connected and (2) edges do not cross each other, except where there is a vertex. Examples. Here are a few examples of connected graphs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
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