Introducing a simple method for detecting the path between two different vertices in the Graphs

Document Type : Original Article

Authors

1 Young Researchers and Elite Club, Arak Branch, Islamic Azad University, Arak, Iran.

2 Department of Computer Science, Arak Branch, Islamic Azad University, Arak, Iran.

3 Department of Mathematics, Shahrekord university, shahrekord, Iran.

Abstract

The problem of path detection in graphs has been proposed from the past up to present, and various solutions have been proposed for this purpose, but it is often not an easy task to implement these methods on a computer. In this paper, a technique for detecting paths in a graph will be introduced using matrix algebra, which makes it possible to implement this rule on a computer. This method can be helpful the optimization of tree-spanning trees in networks. At the end of this study, a numerical example is solved using the proposed method.

Keywords

Main Subjects


[1] A.M. Ahmed, and R. Paulus, Congestion detection technique for multipath routing and load balancing in WSN, Wireless Networks, 3(23) 2017, 881-888.
[2] J.A. Bondy, and U.S.R. Murty, Graph Theory, Graduate Texts in Mathematics, 2008.
[3] N.K. Cauvery, and K.V. Viswanatha, Routing in Dynamic Network using Ants and Genetic Algorithm, International Journal of Computer Science and Network Security(IJCSNS), 3(9) 2009, 194-200
[4] F. Cong, Y. Zhao, The Application of Minimum Spanning Tree Algorithm in the Water Supply Network, International Industrial Informatics and Computer Engineering Conference (IIICEC 2015), 2015, 52-55.
[5] R.P. Grimaldi, Discrete And Combinatorial Mathematics:an applied introduction, Rose-hulman institue of technology, 2005.
[6] H. Jafari, E. Bakhsheshi, and A.R. Feizi-Derakhshi, Presenting a Mathematical Programming Model for Discovering Eulerian Paths (EP) in Certain Specific Graphs, International Journal of Innovation in Engineering, 3(2) 2023, 1-7.
[7] H. Jafari, M. Ehsanifar, and A. Sheykhan, Finding optimum facility’s layout by developed simulated annealing algorithm, International Journal of Research in Industrial Engineering, 9(2), 2020 172-182.
[8] H. Jafari, A.R. Feizi-Derakhshi, and S. Salehfard, Proposing a Pure Binary Linear Programming(PBLP) Model to Discover Eulerian Circuits in Complete Graphs, International Journal of Innovation in Management, Economics and Social Sciences, 3(2) 2023, 52-61.
[9] I.R. Martín, J.J. González, and H. Yaman, A branch-and-cut algorithm for the hub location and routing problem, Computers & Operations Research, 50 2014, 161-174.
[10] N.J. Patel, and R.H. Jhaveri, Trust based approaches for secure routing in VANET: A Survey, Procedia Computer Science, 45, 2015, 592-601.
[11] M. Reimann, M. Laumanns, Savings based ant colony optimization for the capacitated minimum spanning tree problem , Computers & Operations Research , 33, 2006, 1794-1822.