121. 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

122. 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

123. 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.

124. 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(

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

126. 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.

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

128. 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

129. 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

130. Traveling Salesman Problem These pages report the history of the TSP and ongoing work to solve large instances. http://www.tsp.gatech.edu//

131. Eccentric | Facebook as opposed to being normal /li li a href= http//en.wikipedia.org http://www.facebook.com/pages/Eccentric/106071389432406

Eccentric 124 people like this. to connect with Wall Info Fan Photos Eccentric + Others Eccentric Just Others Eccentric joined Facebook. April 4 at 5:43pm See More Posts English (US) Español More… Download a Facebook bookmark for your phone. Login Facebook ©2010

132. Capillary Multi-path Routing With Forward Error Correction By Emin Gabrielyan. http://switzernet.com/people/emin-gabrielyan/060124-capillary-aron-article/

Capillary multi-path routing with Forward Error Correction Emin Gabrielyan Switzernet – EPFL Lausanne Switzerland HTML PDF DOC Table of contents: I. Introduction II. Path Diversity Spread Routing ... Relative links I. Introduction Media streaming is becoming increasingly important in Internet. The major cause for multimedia quality degradation in IP-networks is packet loss. Packet loss occurs in network due to bursts and link failures or packets may be dropped in the application, if they are received too late. Forward Error Correction is a mechanism that may allow the streaming application to overcome losses without utilizing retransmissions. Real-time media or files sent over the internet are chopped into packets, and each packet is either received without error or not received. Packetized communications over internet thus behave like erasure channels and the erasure resilient FEC codes, such as Reed Solomon or another Maximum Distance Separable (MDS) code can be applied on the packet level to a stream of UDP (User Datagram Protocol) data packets. With the proper amount of redundant data included in the stream of transmitted packets, erasure resilient FEC can mitigate the impact of packet loss on the data. For numerous packetized applications, employment of erasure resilient FEC codes offered spectacular results: in satellite feedback-less broadcasts of recurrent voluminous updates of GPS (Global Positioning System) maps to millions of motor vehicles under the condition of arbitrary fragmental visibility due to their locations and trajectories: tunnels, underground parking, buildings and garages [

133. Graph Theory Trees . An acyclic graph (also known as a forest) is a graph with no cycles. A tree is a connected acyclic graph. Thus each component of a forest is tree, and any tree is a http://www.personal.kent.edu/~rmuhamma/GraphTheory/MyGraphTheory/trees.htm

Trees An acyclic graph (also known as a forest) is a graph with no cycles. A tree is a connected acyclic graph. Thus each component of a forest is tree, and any tree is a connected forest. Theorem The following are equivalent in a graph G with n vertices. G is a tree. There is a unique path between every pair of vertices in G. G is connected, and every edge in G is a bridge. G is connected, and it has (n - 1) edges. G is acyclic, and it has (n - 1) edges. G is acyclic, and whenever any two arbitrary nonadjacent vertices in G are joined by and edge, the resulting enlarged graph G' has a unique cycle. G is connected, and whenever any two arbitrary nonadjacent vertices in G are joined by an edge, the resulting enlarged graph has a unique cycle. Generally speaking , algorithms associated with trees can be divided into three types. Algorithms for searching and labeling a given tree. Algorithms for constructing various types of tree. Algorithms for counting trees of a particular type. Tree A tree is a connected graph which contain no cycles.

134. Counting Hamilton Cycles In Product Graphs By Frans Faase. http://www.iwriteiam.nl/counting.html

Counting Hamilton cycles in product graphs This is a subject that has intrigued me as long as I could write computer programs. I have always been interested by seemingly simple problems that result in complex answers. This subject interested me even before I knew it had a name. Actually, it all started with Hamilton paths. The very beginning It all started with a idea that I had, about a program that would draw a snake on the screen. The snake would start at one place in a box, and then extend itself until it could not go further, after which it would shrink again, to seek another path. A snap-shot of the screen could look like: A Fortran program A little later, I wrote a FORTRAN program, that would write down movements that the snake would make, for a certain problem. This would generate output like this: nnnnwsssswnnnnwsssswnnnn wnnn se wnn ssen esw And so on for many pages... (An n stands for going North

135. Math Forum - Problems Library - Discrete Math, Combinatorics TOPICS. This page graph theory . About Levels of Difficulty. Discrete Math combinatorics graph theory logic patterns/recursion proof social choice http://mathforum.org/library/problems/sets/dm_graphtheory.html

Become a Member Learn about Membership TOPICS This page: graph theory About Levels of Difficulty Discrete Math combinatorics graph theory logic patterns/recursion ... PoW Library Teacher Support Page Available Problem Accepts Submissions Discrete Math: Graph Theory Graph theory is a very large topic within discrete mathematics. Graph theory involves working with diagrams that consist of points, called vertices, and line segments, called edges. A few of the topics within graph theory include critical paths (Mud Slides and Critical Paths), minimal cost spanning trees (Minimal Minnie's Cost), Euler paths/circuits (The West Nile Virus Carrying Mosquito Problem), and vertex coloring (Beds of Flowers). The problems below include these types of problems, as well as other problems that involve graphs. For background information elsewhere on our site, explore the High School Discrete Math area of the Ask Dr. Math archives. To find relevant sites on the Web, browse and search Discrete Mathematics in our Internet Mathematics Library.

136. Merlins-World An approach to solve the asymmetric travelling salesman problem using linear optimisation with a polynomial bounded set of constraints. http://www.merlins-world.de

Welcome to the page of M ERLIN The polynomial-bounded solution for the Traveling Salesman Problem You can find here: Something about the background Link to the corresponding article in the journal Applied Mathematics and Computation (Volume 186-1, 1 March 2007, Pg. 907-914) A presentation with a summary description of the MERLIN approach ( pdf Input Files in LP-Format for a linear solver Output Files of the optimization Validation results coming soon... P=NP! © Joachim Mertz, 2006 Contact tsp@merlins-world.de

137. Harmonious Colourings Notes and bibliography by Keith Edwards. http://www.maths.dundee.ac.uk/~kedwards/harmcol.html

Harmonious Colourings and Achromatic Number A vertex colouring of a graph is an assignment of colours to the vertices, with the requirement that adjacent vertices receive distinct colours. A harmonious colouring is a vertex colouring with the added requirement that each pair of colours appears together on at most one edge. The harmonious chromatic number of a graph is the minimum number of colours in a harmonious colouring of the graph. A closely related concept is the achromatic number of a graph, which is the greatest number of colours in a vertex colouring such that for each pair of colours, there is at least one edge whose endpoints have those colours. Such a colouring is called a complete colouring Click here for a bibliography of papers on harmonious colourings and achromatic number (89k, last updated 5 September 2007). This is also available as a pdf file. It is intended to be a comprehensive list; please email me if you know of any omissions or errors, or if you would like a copy of the LaTeX source file. Click here to see a list of my papers on the subject Detachments and Exact Colourings Another related concept is a detachment of a graph. A detachment of a graph G is formed by splitting each vertex into one or more subvertices, and sharing the incident edges arbitrarily among the subvertices. Thus a detachment of G has at least as many vertices as G, and the same number of edges as G.

138. Eric Filiol, Edouard Franc, Alessandro Gubbioli, Benoit Moquet, Guillaume Roblot By Eric Filiol, Edouard Franc, Alessandro Gubbioli, Benoit Moquet and Guillaume Roblot. http://vx.netlux.org/lib/aef05.html

English Deutsch Español Italiano Polski Bookmark VX Heavens Library Collection ... Forum Combinatorial Optimisation of Worm Propagation on an Unknown Network Eric Filiol Edouard Franc Alessandro Gubbioli Benoit Moquet ... Guillaume Roblot PROCEEDINGS OF WORLD ACADEMY OF SCIENCE, ENGINEERING AND TECHNOLOGY VOLUME 23, pp.373-379 ISSN 1307-6884 August 2007 Download PDF (465.73Kb) (You need to be registered on forum Back to index Comments E. Filiol is with the Lab. of Virology and Cryptology, ESAT, B.P. 18, 35998 Rennes Arm´ees (France), Email: eric.filiol@esat.terre.defense.gouv.fr. He is also Full Professor at ESIEA - Laval filiol@esiea.fr Edouard Franc, Benoit Moquet and Guillaume Roblot are with the Lab. of Virology and Cryptology, ESAT, B.P. 18, 35998 Rennes Arm´ees (France) and with the French Navy, ESCANSIC, Saint Mandrier, France. Alessandro Gubbioli is with the Polytecnico di Milano, Milan, Italy and was on stay at the Lab. of Virology and Cryptology, ESAT for this research work. Abstract Worm propagation profiles have significantly changed since 2003-2004: sudden world outbreaks like Blaster or Slammer have progressively disappeared and slower but stealthier worms appeared since, most of them for botnets dissemination. Decreased worm virulence results in more difficult detection. In this paper, we describe a stealth worm propagation model which has been extensively simulated and analysed on a huge virtual network. The main features of this model is its ability to infect any Internet-like network in a few seconds, whatever may be its size while greatly limiting the reinfection attempt overhead of already infected hosts. The main simulation results shows that the combinatorial topology of routing may have a huge impact on the worm propagation and thus some servers play a more essential and significant role than others. The real-time capability to identify them may be essential to greatly hinder worm propagation.

139. Traveling Salesman Problem Generator Generates a Traveling Salesman Problem map and data for a given set of US cities. http://www.60feet6.com/research/usa_tsp_tech.html

TSP Generator Research Sean Forman You Are Here On-line TSP Generator by Sean Forman sforman@sju.edu http://www.sju.edu/~sforman/ Introduction Hamiltonian Circuits and the Traveling Salesman Problem (TSP) are often covered as part of Graph Theory sections in many mathematics courses. TSP is taken from the idea of a salesperson getting up in the morning and then having to visit a large number of clients and then return home at the end of the day. The salesman wishes to find the shortest route to visit all of the clients. Thinking mathematically, this requires the determination of the shortest circuit (a tour that begins and ends in the same city) connecting a given set of cities. Typically, students are introduced to the TSP and shown several common heuristics that can be used to find an approximate (sometimes optimal) solution. I have designed a web application, TSP Generator, that takes as an input a list of user-provided cities (up to 30), and produces a variety of outputs useful to our instructors and students covering this subject. I use this tool as a teaching aid. It allows me to quickly generate example, real-life problems for the students to solve. Given a list of cities, TSP Generator produces the

140. Home - Matrix Graph Grammars Algebraic approach to graph dynamics and graph grammars, using logics, functional analysis and tensor algebra. http://www.mat2gra.info

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