Gourt > Science > Math > Combinatorics > Graph Theory (6)
In mathematics and computer science, graph theory has for its subject matter the properties of graphs. Informally speaking, a graph is a set of objects called points or vertices connected by links called lines or edges. In a graph proper, which is by default undirected, a line from point A to point B is considered to be the same thing as a line from point B to point A. In a digraph, short for directed graph, the two directions are counted as being distinct arcs or directed edges.
Structures that can be represented as graphs are ubiquitous, and many problems of practical interest can be represented by graphs. The link structure of a website could be represented by a directed graph: the vertices are the web pages available at the website and there's a directed edge from page A to page B if and only if A contains a link to B. The development of algorithms to handle graphs is therefore of major interest in computer science.
A graph structure can be extended by assigning a weight to each edge of the graph. Graphs with weights can be used to represent many different concepts; for example if the graph represents a road network, the weights could represent the length of each road.The only information a weighted graph provides as such is (a) the vertices, (b) the edges and (c) the weights. Therefore the example in which the weights represent the roads' lengths doesn't imply that the weights are merely redundant annotations: there is no actual topographical information associated with the graph, so unlike reading a map, measuring the distances between the vertices is completely meaningless -- without the weights, there would be no way of telling what the distance between the vertices is in real life. A digraph with weighted edges is called a network.
More on [ Graph theory ]
@garybernhardt gotcha. I have some ideas from graph theory which may be of use. Memory says that CC can be stated in terms of graphs.
splittingfield (Marc Millstone) Mon, 02 Nov 2009 01:42:21 -0000
@garybernhardt gotcha. I have some ideas from graph theory which may be of use. Memory says that CC can be stated in terms of graphs.
Marking graph theory is funnest
jodoyodo (David Qian) Sun, 01 Nov 2009 21:34:09 -0000
Marking graph theory is funnest
I am spending Halloween night doing stats...what a bore?!? Poor Lars has graph theory homework...grad school will be the death of me!
ramblinglexi (Lexi ) Sun, 01 Nov 2009 00:27:33 -0000
I am spending Halloween night doing stats...what a bore?!? Poor Lars has graph theory homework...grad school will be the death of me!
ploting graph for BODE plot in control theory.there is some doubt that i hv 2 ask wid my teacher...
preety_s (preety kumari) Sat, 31 Oct 2009 20:07:41 -0000
ploting graph for BODE plot in control theory.there is some doubt that i hv 2 ask wid my teacher...
back from "500 days of summer". Washed up and got on my bed. Bedtime story: algorithmic graph theory webcast!
luweidewei (luweidewei) Sat, 31 Oct 2009 16:51:30 -0000
back from "500 days of summer". Washed up and got on my bed. Bedtime story: algorithmic graph theory webcast!
Studying graph theory while babysitting financial/billing jobs on the mainframe, so that I can get paid /and/ understand Karl & Dumont.
clockfort (Chris Lockfort) Sat, 31 Oct 2009 06:56:10 -0000
Studying graph theory while babysitting financial/billing jobs on the mainframe, so that I can get paid /and/ understand Karl & Dumont.
A Constructive Approach to Graph Theory - Notes on a semiotic approach to constructing isomorphism invariants of graphs by John-Tagore Tevet.
404
A Journey through Intersection Graph County - By Erich Prisner.
A Survey of Distance-Transitive Graphs - By Arjeh M. Cohen.
Capillary Multi-Path Routing in a Network of a Directed Symmetric Graph - By Emin Gabrielyan.
Counting Hamilton Cycles in Product Graphs - By Frans Faase.
Fractal Instances of the Traveling Salesman Problem - By Pablo Moscato.
From the Even Cycle Mystery to the L-Matrix Problem and Beyond - By Michael Brundage.
Getgrats: General Theory of Graph Transformation Systems - A research network funded by the European Commission.
Graph Colorings with Local Constraints - A survey by Zsolt Tuza.
Graphnet Archives - Archives of the Graphnet mailing list from February 1990.
404
Graphs: Theory-Algorithms-Complexity - Resource collection maintained by Thomas Emden-Weinert.
500
Harmonious Colourings - Notes and bibliography by Keith Edwards.
Knight's Tour Problem - Solution for chess boards with upto 32 squares.
Multicommodity Problems - Instances and random generators of multicommodity flow and network design problems.
Network Resources for Colouring a Graph - Resources for formulating and solving coloring problems.
Other Graph Theory and Related Pages - Miscellaneous pages collected by Stephen C. Locke.
Parameters of Directed Strongly Regular Graphs - Parameters, constructions and nonexistence information for directed strongly regular graphs.
Regular Graphs Page - Tables of simple connected k-regular graphs on n vertices and girth at least g.
Meta Description: [ Regular Graphs Page ]
Sandpiles in Graphs - An application of cellular automata by Angela R. Kerns.
Meta Description: [ Sandpiles in Graphs ]
Signed, Gain and Biased Graphs - List of publications and manuscripts annotated by Thomas Zaslavsky.
Spectral Graph Theory - People, publications, research topics, open problems, events and resources.
Meta Description: [ The theory of graph spectra can, in a
way, be considered as an attempt to utilize linear algebra including,
in particular, the well-developed theory of matrices for the purposes
of graph theory and its applications. ]
404
The Four Color Theorem - Computer aided proof of the four color theorem by Neil Robertson, Daniel P. Sanders, Paul Seymour and Robin Thomas.
The Hamiltonian Page - Hamiltonian cycle and path problems, their generalisations and variations.
404
Thrackles - Jon Perry's pages on the thrackle conjecture.
Traveling Salesman Problem - These pages report the history of the TSP and ongoing work to solve large instances.
TSP Generator - Generates a Traveling Salesman Problem map and data for a given set of US cities.
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