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.
| Published in | Engineering Mathematics (Volume 3, Issue 1) |
| DOI | 10.11648/j.engmath.20190301.11 |
| Page(s) | 1-5 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2019. Published by Science Publishing Group |
Arc Routing, Konigsberg Bridge Problem, Graph Theory, Euler’s Theorem Applications, Fortran Coding
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| [8] | Dror, M. (Ed.). (2012). Arc routing: theory, solutions and applications. Springer Science & Business Media. |
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APA Style
Hashnayne Ahmed. (2019). Graph Routing Problem Using Euler’s Theorem and Its Applications. Engineering Mathematics, 3(1), 1-5. https://doi.org/10.11648/j.engmath.20190301.11
ACS Style
Hashnayne Ahmed. Graph Routing Problem Using Euler’s Theorem and Its Applications. Eng. Math. 2019, 3(1), 1-5. doi: 10.11648/j.engmath.20190301.11
AMA Style
Hashnayne Ahmed. Graph Routing Problem Using Euler’s Theorem and Its Applications. Eng Math. 2019;3(1):1-5. doi: 10.11648/j.engmath.20190301.11
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Download@article{10.11648/j.engmath.20190301.11,
author = {Hashnayne Ahmed},
title = {Graph Routing Problem Using Euler’s Theorem and Its Applications},
journal = {Engineering Mathematics},
volume = {3},
number = {1},
pages = {1-5},
doi = {10.11648/j.engmath.20190301.11},
url = {https://doi.org/10.11648/j.engmath.20190301.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.engmath.20190301.11},
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.},
year = {2019}
}
TY - JOUR T1 - Graph Routing Problem Using Euler’s Theorem and Its Applications AU - Hashnayne Ahmed Y1 - 2019/06/26 PY - 2019 N1 - https://doi.org/10.11648/j.engmath.20190301.11 DO - 10.11648/j.engmath.20190301.11 T2 - Engineering Mathematics JF - Engineering Mathematics JO - Engineering Mathematics SP - 1 EP - 5 PB - Science Publishing Group SN - 2640-088X UR - https://doi.org/10.11648/j.engmath.20190301.11 AB - 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. VL - 3 IS - 1 ER -
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