61. Problems In Topological Graph Theory Web text by Dan Archdeacon with a list of open questions in topological graph theory. http://www.emba.uvm.edu/~archdeac/newlist/problems.html

Problems in Topological Graph Theory Go to the Table of Contents Compiled by Dan Archdeacon List Started: August 5, 1995 Converted to the web: September 1, 1998 Last modified: November 15, 1998 E-Mail: dan.archdeacon@uvm.edu Postal Mail: Dan Archdeacon Dept. of Math. and Stat. University of Vermon t Burlington VT 05401-1455 USA Abstract Do you think you've got problems? I know I do. This paper contains an ongoing list of open questions in topological graph theory. If you are interested in adding a problem to this list please contact me at the addresses above. The spirit is inclusive-don't submit a problem you're saving for your graduate student. If it appears here, it's fair game. If you solve one of the problems, know some additional history, or recognize it as misphrased or just a stupid question, please let me know so that I can keep the list up-to-date. I've taken quite a bit of liberty editing the submissions. I apologize for any errors introduced. Enjoy my problems-I do! Table of Contents Classical questions on genus Coloring graphs and maps Drawings and crossings Paths, cycles, and matchings

62. Graph Theory Graph Theory is a 2005 commission of the New Radio and Performing Arts, Inc., (aka Ether Ore) for its Turbulence web site. It was made possible with funding from the Greenwall http://www.turbulence.org/Works/graphtheory/

63. Regular Graphs Page Tables of simple connected k-regular graphs on n vertices and girth at least g. http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html

Regular Graphs The following tables contain numbers of simple connected k -regular graphs on n vertices and girth at least g with given parameters n,k,g . If a number in the table is a link, then you can get further information about the graphs including adjacency lists or shortcode files. A description of the shortcode coding can be found in the GENREG-manual Most of the numbers were obtained by the computer program GENREG. It does not only compute the number of regular graphs for the chosen parameters but even constructs the desired graphs. The large cases with k=3 were solved by Gunnar Brinkmann (University of Ghent), who implemented a very efficient algorithm for cubic graphs. If you want to compute regular graphs on your own or perhaps try one of the unsolved cases, you can get a free version of the generator. There are executables available for DEC-Alpha SGI Workstations and Linux Win NT PCs. The package genreg.tar contains a makefile for easy installation on any UNIX machine. There is a german and an english latex version of the manual included as well as a short C-programm that demonstrates how to read shortcode files. When using GENREG for your publications, please cite

64. Games On Graphs Overview Graphs are mathematical objects that are made of dots connected by lines. Graph Theory is the branch of mathematics that involves the study of graphs. http://www.c3.lanl.gov/mega-math/workbk/graph/graph.html

Overview Graphs are mathematical objects that are made of dots connected by lines. Graph Theory is the branch of mathematics that involves the study of graphs. Graphs are very powerful tools for creating mathematical models of a wide variety of situations. Graph theory has been instrumental for analyzing and solving problems in areas as diverse as computer network design, urban planning, and molecular biology. Graph theory has been used to find the best way to route and schedule airplanes and invent a secret code that no one can crack. The Big Picture

65. Sandpiles In Graphs An application of cellular automata by Angela R. Kerns. http://www.cs.wvu.edu/~angela/cs418a/cs418a.html

Next: Introduction: Sandpiles in Graphs Sandpiles in Graphs Angela R. Kerns Department of Statistics and Computer Science West Virginia University angela@cs.wvu.edu Introduction: Sandpiles in Graphs Cellular Automata Models of Real Sandpiles The Basic Sandpile Model The Graph ... About this document ... Angela Kerns Thu Dec 5 15:22:37 EST 1996

66. Graph Theory Introduction of Graph Theory. EMAT 6690. YAMAGUCHI, Junichi . In the sprign semester 2005, I take the mathematics course named Graph Theory(MATH6690). http://jwilson.coe.uga.edu/EMAT6680/Yamaguchi/emat6690/essay1/GT.html

Introduction of Graph Theory EMAT 6690 YAMAGUCHI, Jun-ichi In the sprign semester 2005, I take the mathematics course named "Graph Theory(MATH6690)." This course is hard but very interesting and open my eyes to new mathematical world. I have loved study Graph theory and really want you to study this very young mathematics. This field of mathematics can be applied for many issues, rainging from operational research and chemistry to genetics and linguistics, and from electrical engineering and geography to sociology and architecture. What is Graph Theory? Graph theory concerns the relationship among lines and points. A graph consists of some points and some lines between them. No attention is paid to the position of points and the length of the lines. Thus, the two graphs below are the same graph. You can get more detailed information of graph theory at this site (http://www.netipedia.com/index.php/Graph_theory) Basic Terms of Graph Theory a SIMPLE graph G is one satisfying that; (1)having at most one edge (line) between any two vertices (points) and

67. Network Resources For Coloring A Graph Resources for formulating and solving coloring problems. http://mat.gsia.cmu.edu/COLOR/color.html

Network Resources for Coloring a Graph by: Michael Trick (trick@cmu.edu) Last Update: October 26, 1994 Introduction Given an undirected graph, a clique of the graph is a set of mutually adjacent vertices. A maximum clique is, naturally, a clique whose number of vertices is at least as large as that for any other clique in the graph. If the vertices have weights then a maximum weighted clique is a clique with the largest possible sum of vertex weights. A (vertex) coloring of an undirected graph is an assignment of a label to each node. It is required that the labels on the pair of nodes incident to any edge be different. A minimum coloring of a graph is a coloring that uses as few different labels as possible. Clique and coloring problems are very closely related. It is straightforward to see that the size of the maximum clique is a lower bound on the minimum number of labels needed to color a graph. Many problems of practical interest can be modeled as clique and coloring problems. The general form of these applications involves forming a graph with nodes representing items of interest. An edge connects two ``incompatible'' items. The maximum clique problem is then to find as large a set of pairwise incompatible items as possible. The minimum coloring problem is to assign a color to each item so that every incompatible pair is assigned different colors. This document tries to bring together the various resources that are available on the Internet to help in formulating and solving coloring problems.

68. Graph Theory ORNotes J E Beasley. OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research (OR). http://people.brunel.ac.uk/~mastjjb/jeb/or/graph.html

OR-Notes J E Beasley OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research (OR). They were originally used by me in an introductory OR course I give at Imperial College. They are now available for use by any students and teachers interested in OR subject to the following conditions A full list of the topics available in OR-Notes can be found here Graph theory Introduction Graph theory deals with problems that have a graph (or network) structure. In this context a graph (or network as many people use the terms interchangeable) consists of: vertices/nodes - which are a collection of points; and arcs - which are lines running between the nodes. Such arcs may be directed or undirected and undirected arcs are often called links or edges. An example graph is shown below. Graph theory is used in dealing with problems which have a fairly natural graph/network structure, for example: road networks - nodes = towns/road junctions, arcs = roads communication networks - telephone systems computer systems foreign exchange/multinational tax planning (network of fiscal flows) Note here that the minimum cost network flow problem (also dealt with in this course) is an example of a problem with a graph/network structure.

69. Home Page Of Signed Graphs List of publications and manuscripts annotated by Thomas Zaslavsky. http://www.math.binghamton.edu/zaslav/Bsg/

The Home Page of Signed, Gain, and Biased Graphs by Thomas Zaslavsky Why is this picture appropriate? Illustration by Hugh Thomson, courtesy of Henry Churchyard Mathematical Bibliography A Mathematical Bibliography of Signed and Gain Graphs and Allied Areas Dynamic Surveys in Combinatorics of the Electronic Journal of Combinatorics. Seventh Edition, 1999 September 22. vi + 151 pp. Download the preliminary 8th edition, vi + 249 pp., in PostScript (2 MB) or PDF (2 MB), or the Tex file A signed graph is a graph with signs labelling its edges. A gain graph has elements of any group as edge labels (called "gains"), with the understanding that reversing the sense in which you traverse the edge will invert the gain. A bidirected graph has both ends of each edge directed independently; it can be regarded as an oriented signed graph. This is a classified and copiously annotated list of all the publications (and suitable unpublished manuscripts, theses, etc.) of mathematical interest related to signed graphs, vertex-signed graphs, gain graphs, and bidirected graphs that I've been able to find and examine and enter into the list. It includes all or part of the literature of signed digraphs, Dowling lattices, combinatorics of root systems, parity of cycles and paths and max-cut problems (these concern all-negative signatures), generalized networks (networks with gains), qualitative matrix theory, quadratic pseudo-Boolean functions, dynamic labeled 2-structures, etc., etc., as well as selected publications on applications to social science (psychology, sociology, anthropology, economics) and natural science (physics, chemistry, biologysorry, no geology or astronomy-yet).

70. Multicommodity Problems Instances and random generators of multicommodity flow and network design problems. http://www.di.unipi.it/di/groups/optimize/Data/MMCF.html

Multicommodity Problems Last update: 25/08/2010 This page provides a collection of instances and random generators of Multicommodity Flow problems. The page comprises: Linear Multicommodity Flow problems, ordinary LPs but challenging due to their size; NonLinear Multicommodity Flow problems, difficult both for their size and the nonlinearity of the objective function; Multicommodity Network Design problems, difficult both for their size and the presence of integer variables; Some links to similar pages around the web; A small bibliography of the articles where the instances have been tested. All instances are packed with "tar" and compressed with "gzip"; these are ubiquitous on unix systems, and available for essentially every other architecture. Once a file f .tar.gz has been downloaded, it must be first decompressed (gzip -d f .tar.gz under unix) and then un-tarred (tar xvf f .tar under unix) to retrieve the original files and/or directories. Files of the type f .tgz are compressed by the tar command, and can be decompressed and un-tarred at the same time (tar xzvf f .tgz). A service C++ class for (MMCF)-solvers

71. Graph Theory Graph Theory Graph theory is a flourishing discipline containing a body of beautiful and powerful theorems of wide applicability. Its explosive growth in recent years is mainly http://www.springer.com/mathematics/numbers/book/978-1-84628-969-9

Basket USA Change New User Login Home ... My Springer Manage your Account Change Email or Postal Address Change Password Password Lost? Manage your Alerts Change alert profile Unsubscribe Article Tracking Online Book Review Copies ... Subjects Choose a discipline: Astronomy Biomedical Sciences Chemistry Computer Science ... Services Find all our services for you Authors Booksellers Book Reviews Librarians ... Subscription Agencies We are happy to help you! Manage your Account Online Exam Copies Order process Our Email Services SpringerAlerts Overview SpringerAlerts for Journals SpringerAlerts for Book Series SpringerAlerts for Books ... SpringerAlerts for Booksellers More about: Spektrum Akademischer Verlag Birkhäuser T.M.C. Asser Press Publishers and Imprints with external Websites Apress BioMed Central Codes Rousseau Etrasa ... About us Company Information Mission Statement Management Annual Reports Key Facts ... Locations Worldwide What we do Publishing Fields Springer and Open Access Springer in China Developing Countries Initiative Press Press Releases Springer Select Media Kit and Downloads Career All Job Vacancies Trainee-Programs / Editorial Trainees Internships Vocational Training There are no results matching your search terms.

72. Archives Of GRAPHNET@LISTSERV.NODAK.EDU Archives of the Graphnet mailing list from February 1990. http://listserv.nodak.edu/archives/graphnet.html

List Archives Subscriber's Corner Server Archives List Archives List Management List Moderation Server Management Help ... Archive Search Archives of GRAPHNET@LISTSERV.NODAK.EDU GRAPHNET - Graph Theory Search the archives Post to the list Join or leave the list (or change settings) Manage the list (list owners only) October 2010 September 2010 August 2010 July 2010 ... LISTSERV.NODAK.EDU

73. Introduction To Graph Theory Section1 Introduction 4 1. Introduction A graph isamathematical object that captures the notion of connection. Most people are familiar with the children'spuzzleoftrying to http://www.southernct.edu/~fields/TeX-PDF/GraphTheory.pdf

74. GETGRATS Home Page A research network funded by the European Commission. http://www.di.unipi.it/~andrea/GETGRATS/

GETGRATS General Theory of Graph Transformation Systems a Research Network funded by the European Community Introduction Research Objectives Events Participants ... APPLIGRAPH (an ESPRIT Working Group closely related to GETGRATS) Introduction GETGRATS (General Theory of Graph Transformation Systems) is a Research TMR Network funded by the European Commission, consisting of seven research groups that are listed here together with the corresponding team leader: University of Antwerp - UIA (Belgium): Prof. Dr. Dirk Janssens Technische Universitaet Berlin - TUB (Germany): Prof. Dr. Hartmut Ehrig Laboratoire Bordelais de Recherche en Informatique - LaBRI (France): Prof. Dr. Michel Bauderon Universitaet Bremen - UNIBREMEN (Germany): Prof. Dr. Hans-Joerg Kreowski University of Leiden - RUL (The Netherlands): Prof. Dr. Grzegorz Rozenberg - UNIPISA (Italy) [main contractor]: Prof. Ugo Montanari - UNIROMA1 (Italy): Prof. Dr. Francesco Parisi Presicce The Network Coordinator is Andrea Corradini (Pisa). Research Objectives The aim of the project is to develop a General Theory of Graph Transformation Systems (GTS) by solidifying the use of mathematics in their study and regarding them as the objects of discourse and interest. Particular emphasis will be placed on the comparison, combination, and unification of the various approaches to graph rewriting, where the involved partners have considerable expertise.

75. A Survey Of Distance-Transitive Graphs By Arjeh M. Cohen. http://www.win.tue.nl/~amc/oz/dtg/survey.html

A Survey of Distance-Transitive Graphs by Arjeh M. Cohen last update Aug 2001 Preface This is a survey of the state of the art of the classification of primitive distance transitive graphs. It might help to carry out the remainder of the work, as sketched at the DTG workshop in Eindhoven, December 1998. The open cases are listed in three tables, to be found from within the text below. Introduction Starting point is the following Theorem [PSY] Let X V E ) be a primitive distance-regular graph with a distance-transitive group G of automorphisms. Assume k, d X is a Hamming graph and G is a wreath product; ... V (See [VBt] for another proof.) The theorem shows how to use the classification of finite simple groups for the determination of all primitive distance-transitive graphs. In view of the determination of all rank 3 groups (see e.g. ), we may assume diam X Case i. Here the graph X is well known, although the possibilities for the group G are not completely determined. Case ii. G almost simple The classification of finite simple groups can be invoked to make a further subdivision according to the possibilities for soc( G ). Knowledge of the maximal subgroups of soc(

76. Knight Tour Solution for chess boards with up to 32 squares. http://www.tri.org.au/knightframe.html

77. No. 2467: Graph Theory Graph Theory and the K nigsberg Bridge Problem Today, the bridges of K nigsberg. The University of Houston’s College of Engineering presents this series about the http://www.uh.edu/engines/epi2467.htm

No. 2467 GRAPH THEORY by Andrew Boyd Click here for audio of Episode 2467 machines that make our civilization run, and the people whose ingenuity created them. I “Pick any island,” she said, “and see if you can find a walk that goes over every bridge exactly once and brings you back to the island where you started.” I tried one walk, then another. No luck. I always had to retrace at least one bridge. I drew the picture on a piece of paper and took it home to show my parents. The instructor had succeeded. She’d made me think. I ran into the problem many years later in a college course on graph theory . To mathematicians, a graph is a collection of islands connected by bridges or, more precisely, points connected by lines. Get a sheet of paper. Draw some points. Connect some of them with lines. You’ve got what mathematicians call a graph. Pretty simple. But graphs turn out to be remarkably interesting. Many mathematicians make their living trying to solve difficult, abstract problems about graphs. Claws. Odd holes. Odd anti-holes. Graph theorists speak a language of their own. But graph theory has plenty of practical problems, too. For example, street maps define graphs. We can think of each intersection as a point and each street segment between two intersections as a line. So the problem of finding a shortest path from your house to work is a problem in graph theory. So is the problem of picking good bus routes, or how to make scheduled deliveries from a warehouse. Can garbage trucks be routed so they don’t go down a street more than once? Graph theory again. In fact, it’s just the island-and-bridge problem stated more generally.

78. Fractal Instances Of The Traveling Salesman Problem By Pablo Moscato. http://www.ing.unlp.edu.ar/cetad/mos/FRACTAL_TSP_home.html

79. Graph Theory Definitions and Examples . Informally, a graph is a diagram consisting of points, called vertices, joined together by lines, called edges; each edge joins exactly two vertices. http://www.personal.kent.edu/~rmuhamma/GraphTheory/MyGraphTheory/defEx.htm

Definitions and Examples Informally, a graph is a diagram consisting of points, called vertices, joined together by lines, called edges; each edge joins exactly two vertices. A graph G is a triple consisting of a vertex set of V( G ), an edge set E(G), and a relation that associates with each edge two vertices (not necessarily distinct) called its endpoints. Definition of Graph Formally, a graph G is an ordered pair of dsjoint sets (V, E), where E V V. Set V is called the vertex or node set, while set E is the edge set of graph G. Typically, it is assumed that self-loops (i.e. edges of the form (u, u), for some u V) are not contained in a graph. Directed and Undirected Graph A graph G = (V, E) is directed if the edge set is composed of ordered vertex (node) pairs. A graph is undirected if the edge set is composed of unordered vertex pair. Vertex Cardinality The number of vertices, the cardinality n m to denote the size of G. Neighbor Vertex and Neighborhood We write v i v j i , v j E(G), and if e = v

80. Parameters Of Directed Strongly Regular Graphs Parameters, constructions and nonexistence information for directed strongly regular graphs. http://homepages.cwi.nl/~aeb/math/dsrg/dsrg.html

Next Previous Contents Parameters of directed strongly regular graphs aeb We give parameters, constructions and nonexistence information for directed strongly regular graphs as defined by Duval Definition Hadamard matrices The 2-dimensional case The 1-dimensional case ... Next Previous Contents

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