Archive
Special Issues
Graph Routing Problem Using Euler’s Theorem and Its Applications
Engineering Mathematics
Volume 3, Issue 1, June 2019, Pages: 1-5
Received: May 16, 2019; Accepted: Jun. 17, 2019; Published: Jun. 26, 2019
Author
Hashnayne Ahmed, Department of Mathematics, University of Barishal, Barishal, Bangladesh
Article Tools
Abstract
In this modern era, time and cases related to time is very important to us. For shortening time, Eulerian Circuit can open a new dimension. In computer science, social science and natural science, graph theory is a stimulating space for the study of proof techniques. Graphs are also effective in modeling a variety of optimization cases like routing protocols, network management, stochastic approaches, street mapping etc. Konigsberg Bridge Problem has seven bridges linked with four islands detached by a river in such a way that one can’t walk through each of the bridges exactly once and returning back to the starting point. Leonard Euler solved it in 1735 which is the foundation of modern graph theory. Euler’s solution for Konigsberg Bridge Problem is considered as the first theorem of Graph Theory which gives the idea of Eulerian circuit. It can be used in several cases for shortening any path. From the Konigsberg Bridge Problem to ongoing DNA fragmentation problem, it has its applications. Aiming to build such a dimension using Euler’s theorem and Konigsberg Bridge Problem, this paper presents about the history of remarkable Konigsberg Bridge Problem, Euler’s Explanation on it, an alternative explanation and some applications to Eulerian Circuit using graph routing and Fortran Coding of it.
Keywords
Arc Routing, Konigsberg Bridge Problem, Graph Theory, Euler’s Theorem Applications, Fortran Coding
Hashnayne Ahmed, Graph Routing Problem Using Euler’s Theorem and Its Applications, Engineering Mathematics. Vol. 3, No. 1, 2019, pp. 1-5. doi: 10.11648/j.engmath.20190301.11
References
[1]
Gurjar, M. Applications of Euler’s Theorem.
[2]
Sanabria, S. Königsberg Bridge Problem.
[3]
Euler, L. (1741). Solutio problematis ad geometriam situs pertinentis. Commentarii academiae scientiarum Petropolitanae, 128-140.
[4]
Shields, R. (2012). Cultural topology: The seven bridges of Königsburg, 1736. Theory, Culture & Society, 29 (4-5), 43-57.
[5]
Ismail, A. S., Hasni, R., & Subramanian, K. G. (2009). Some applications of Eulerian graphs. International Journal of Mathematical Science Education, 2 (2), 1-10.
[6]
Rosen, K. H., & Krithivasan, K. (2012). Discrete mathematics and its applications: with combinatorics and graph theory. Tata McGraw-Hill Education.
[7]
Gross, J. L., & Yellen, J. (2005). Graph theory and its applications. Chapman and Hall/CRC.
[8]
Dror, M. (Ed.). (2012). Arc routing: theory, solutions and applications. Springer Science & Business Media.
[9]
Biggs, N., Lloyd, E. K., & Wilson, R. J. (1986). Graph Theory, 1736-1936. Oxford University Press.
[10]
Paoletti, T. (2011). Leonard Euler’s solution to the Königsberg bridge problem. URL http://www. maa.org/press/periodicals/convergence/leonard-eulers-solution-to-the-konigsberg-bridge-problem. (Cited on pages 9 and 10).
[11]
Eiselt, H. A., Gendreau, M., & Laporte, G. (1995). Arc routing problems, part I: The Chinese postman problem. Operations Research, 43 (2), 231-242.
PUBLICATION SERVICES