# Graph theory

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

## 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;...

## References

- [1]Biggs, N.L., Lloyd, E.K., and Wilson, R.J. (1976). Graph Theory 1736–1936, Clarendon Press, Oxford.Google Scholar
- [2]Bondy, J.A. and Murty, U.S.R. (1979). Graph Theory with Applications, Elsevier, New York.Google Scholar
- [3]Diestel, R. (1997). Graph Theory, Springer, New York.Google Scholar
- [4]Evans, J.R. and Minieka, E. (1992). Optimization Algorithms for Networks and Graphs, Marcel Dekker, New York.Google Scholar
- [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.Google Scholar
- [6]Michaels, J.G. and Rosen, K.H. (1991). Applications of Discrete Mathematics, McGraw-Hill, New York.Google Scholar
- [7]Roberts, F. (1976). Discrete Mathematical Models, with Applications to Social, Biological, and Environmental Problems, Prentice-Hall, Englewood Cliffs, New Jersey.Google Scholar
- [8]West, D.B. (1996). Introduction to Graph Theory, Prentice-Hall, Upper Saddle River, New Jersey.Google Scholar
- [9]Wilson, R.J. and Watkins, J.J. (1990). Graphs: An Introductory Approach, John Wiley, New York.Google Scholar