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Encyclopedia of Operations Research and Management Science pp 339–342Cite as

Graph theory

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INTRODUCTION

Graph theory is the general study of the interconnection of various elements. While the origins of graph theory can be traced back to the eighteenth century, this area of discrete mathematics has experienced most of its tremendous growth during the past few decades. This rapid growth, both in the development of new theory and applications, reflects the fact that graphs can model a wide variety of natural and technological systems.

A number of physical systems can be viewed as graphs, composed of nodes (or vertices) connected together by edges(or arcs). For example, a local area computer network defines a graph whose nodes represent individual computers (or peripheral devices) and whose edges represent the physical cables connecting such computers. A telecommunication net-work consists of telephone locations (and central switching stations) joined by sections of copper wire (and optical fibers); an airline system has airports as its nodes and direct flights as its edges;...

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References

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  5. Fulkerson, D.R. (1975). Studies in Graph Theory, Parts I–II, volumes 11–12, MAA Studies in Mathematics. Mathematical Association of America, Washington, DC.

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  6. Michaels, J.G. and Rosen, K.H. (1991). Applications of Discrete Mathematics, McGraw-Hill, New York.

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  7. Roberts, F. (1976). Discrete Mathematical Models, with Applications to Social, Biological, and Environmental Problems, Prentice-Hall, Englewood Cliffs, New Jersey.

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  8. West, D.B. (1996). Introduction to Graph Theory, Prentice-Hall, Upper Saddle River, New Jersey.

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  9. Wilson, R.J. and Watkins, J.J. (1990). Graphs: An Introductory Approach, John Wiley, New York.

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Author information

Authors and Affiliations

  1. Clemson University, South Carolina, USA

    Douglas R. Shier

Authors
  1. Douglas R. Shier
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Editor information

Editors and Affiliations

  1. Robert H. Smith School of Business, University of Maryland, College Part, Maryland, USA

    Saul I. Gass

  2. School of Information Technology & Engineering, George Mason University, Fairfax, Virginia, USA

    Carl M. Harris

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© 2001 Kluwer Academic Publishers

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Shier, D.R. (2001). Graph theory . In: Gass, S.I., Harris, C.M. (eds) Encyclopedia of Operations Research and Management Science. Springer, New York, NY. https://doi.org/10.1007/1-4020-0611-X_402

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  • DOI: https://doi.org/10.1007/1-4020-0611-X_402

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-7923-7827-3

  • Online ISBN: 978-1-4020-0611-1

  • eBook Packages: Springer Book Archive

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