Graph Theory; History, Applications, and, Vision

Document Type : Promotional Paper

Author

Department of Mathematics, University of Applied Science and Technology (UAST), Tehran, IRAN

Abstract

Graph theory is a leading theory in mathematics, which is used in many sciences. In this article, by stating the history of this, its expansion and development, we have mentioned the course of famous problems in graph theory. Also, a practical application of this theory is stated.

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Main Subjects


[1] K. Appel and W. Haken, Every planar map is four colorable, Illinois Journal of Mathematics, 21 (1977) 439–597.
[2] M. Behzad and G. Chartrand, Introduction to the theory of graphs, Allyn and Bacon: Boston, 1971.
[3] N. Biggs, Algebraic Graph Theory, Second edition, Cambridge University Press, Cambridge, 1993.
[4] B. Bollobás, Extremal Graph Theory, Academic Press, 1978.
[5] J. A. Bondy and U. S. R. Murty, Graph Theory, Graduate: Texts in Mathematics, Springer, New York, 2008.
[6] F. E. Browder (editor), Mathematical Developments Arising from Hilbert Problems, Proceedings of Symposia in Pure Mathematics, 28 (Part 1), American Mathematical Society, Providence, 1976.
[7] A. Cayley and M. Philos, 1874, 47, 444–446, as quoted in N. L. Biggs, E. K. Lloyd and R. J. Wilson, Graph Theory 1736–1936, Clarendon Press, Oxford, 1976; Oxford, University Press, 1986.
[8] G. Chartrand, L. Lesniak and P. Zhang, Graphs & digraphs, (5th ed.), CRC Press, 2012.
[9] R. Diestel, Graph theory (5th ed.), Springer, 2017.
[10] L. Euler, Solutio problematis ad geometriam situs pertinentis, Comment. Acad. Sci. U Petrop, 8 (1736) 28–40.
[11] C. Godsil and G. Royle, Algebraic Graph Theory, Graduate Texts in Mathematics, Springer–Verlag, New York, 2001.
[12] F. Harary, Graph theory, Addison-Wesley, 1969.
[13] D. Hilbert; Mathematical problems, Bulletin of the American Mathematical Society, 8 (1902) 437–479.
[14] K. Kuratowski, Sur le probléme des courbes gauches en topologie, Fund Math, 15 (1930) 271–283.
[15] j. O’Connor and E. F. Robertson, The Four Colour Theorem, 1996. Web. 2 Apr. 2015. http://www-history.mcs.st-and.ac.uk/HistTopics/Thefour
[16] A. J. Schwenk and R. J. Wilson, On the eigenvalues of a graph, Selected Topics in Graph Theory, (1978) 307–336.
[17] C. Thomassen, Kuratowski’s theorem, J. Graph Theory, 5 (1981) 225–241.
[18] G. Wanner, H. Gerhard and E. Hairer, Analysis by its history, (1st ed.), Springer Publishing, 2005.
[19] D. West, Introduction to graph theory, Prentice Hall, 2001.