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Graph_theory (including recent related patents.)
Graph theoryGraph theory is the branch of mathematics that examines the properties of graphs. A graph with 6 vertices and 7 edges. Informally, a graph is a set of objects called vertices (or nodes) connected by links called edges (or arcs). Typically, a graph is depicted as a set of dots (i.e., vertices) connected by lines (i.e., edges). For more and formal definitions, see Glossary of graph theory and Graph (mathematics). Depending on the applications, edges may or may not have a direction; edges joining a vertex to itself may or may not be allowed, and vertices and/or edges may be assigned weights, that is, numbers. If the edges have a direction associated with them (indicated by an arrow in the graphical representation) then it is a directed graph, or digraph. A graph with only one vertex and no edges is the trivial graph or "the dot". Structures that can be represented as graphs are ubiquitous, and many problems of practical interest can be formulated as questions about certain graphs. Various networks are conveniently described by means of graphs. For example, the link structure of Wikipedia could be represented by a directed graph: the vertices are the articles in Wikipedia and there's a directed edge from article A to article B if and only if A contains a link to B. Directed graphs are also used to represent finite state machines. The development of algorithms to handle graphs is therefore of major interest in computer science. Table of contents showTocToggle("show","hide") 1 History 2 Graph problems 3 Important algorithms 4 Generalizations 5 Related areas of mathematics 6 See also 7 External links History Leonhard Euler's paper on Seven Bridges of Königsberg is considered to be the first result in graph theory. It is also regarded as one of the first topological results in geometry; that is, it does not depend on any measurements. This illustrates the deep connection between graph theory and topology. Graph problems
This article is adapted from from Wikipedia All Wikipedia article text is available under the terms of the GNU Free Documentation License Six Degrees: The Science of a Connected Age by Duncan J. Watts Introductory Graph Theory by Gary Chartrand College Algebra Enhanced with Graphing Utilities (3rd Edition) by Michael Sullivan Classification and Regression Trees by Leo Breiman Handbook of Graphs and Networks : From the Genome to the Internet by Stefan Bornholdt Schaum's Outline of Graph Theory: Including Hundreds of Solved Problems by V. K. Balakrishnan Algebraic Graph Theory by Norman Biggs Introduction to Graph Theory by Richard J. Trudeau Data Structures and Network Algorithms (CBMS-NSF Regional Conference Series in Applied Mathematics) by R.E. Tarjan A Graphical Approach to College Algebra (3rd Edition) by John Hornsby Graph Theoretical Models of Abstract Musical Transformation : An Introduction and Compendium for Composers and Theorists by Jeffrey Johnson Discrete Mathematics with Graph Theory (2nd Edition) by Edgar G. Goodaire Applied Combinatorics by Alan Tucker Computational Discrete Mathematics : Combinatorics and Graph Theory with Mathematica ® by Sriram Pemmaraju Graph Drawing: Algorithms for the Visualization of Graphs by Ioannis G. Tollis Recent Graph_theory related patents From USPTO: |
