On applications of bipartite graph associated with algebraic structures-Reference-Cited by-同舟云学术

On applications of bipartite graph associated with algebraic structures

Published:2020-01-01 Issue:1 Volume:18 Page:57-66
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Zhang Xiujun¹,Nadeem Muhammed²,Ahmad Sarfraz³,Siddiqui Muhammad Kamran³

Affiliation:

1. Key Laboratory of Pattern Recognition and Intelligent Information Processing, Institutions of Higher Education of Sichuan Province , Chengdu University , Chengdu , 610106 , China

2. Sharif College of Engineering and Technology , Lahore , 54000 , Pakistan

3. Department of Mathematics , Comsats University Islamabad, Lahore Campus , Lahore , Pakistan

Abstract

Abstract The latest developments in algebra and graph theory allow us to ask a natural question, what is the application in real world of this graph associated with some mathematical system? Groups can be used to construct new non-associative algebraic structures, loops. Graph theory plays an important role in various fields through edge labeling. In this paper, we shall discuss some applications of bipartite graphs, related with Latin squares of Wilson loops, such as metabolic pathways, chemical reaction networks, routing and wavelength assignment problem, missile guidance, astronomy and x-ray crystallography.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2020-0003/pdf

Reference33 articles.

1. E.G. Goodaire and D.A. Robinson, Some special conjugacy closed loops, Canad. Math. Bull. 33 (1990), no. 1, 73–78, 10.4153/CMB-1990-013-9.

2. M.J. Osborn, Loops with the weak inverse property, Pacific J. Math. 10 (1960), no. 1, 295–304, 12.2153/CMB-1960-015-7.

3. R. Artzy, Inverse-cycles in weak-inverse loops, Proc. Amer. Math. Soc. 68 (1978), no. 2, 132–134, 10.1090/S0002-9939-1978-0463340-4.

4. A. Drapal, Conjugacy closed loops and their multiplication groups, J. Algebra 272 (2004), no. 2, 838–850, 10.1016/j.jalgebra.2003.06.011.

5. E.L. Wilson, A class of loops with the isotopy-isomorphy property, Canad. J. Math. 18 (1966), 589–592, 10.4153/CJM-1966-057-0.

Cited by 6 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Graphs Connected to Isotopes of Inverse Property Quasigroups: A Few Applications;Journal of Applied Mathematics;2024-01

2. A New Graphical Representation of the Old Algebraic Structure;Journal of Mathematics;2023-07-06

3. On Bipartite Circulant Graph Decompositions Based on Cartesian and Tensor Products with Novel Topologies and Deadlock-Free Routing;Algorithms;2022-12-22

4. On Characterization of Graphs Structures Connected with Some Algebraic Properties;Mathematical Problems in Engineering;2022-06-08

5. A Class of Koszul Algebra and Some Homological Invariants through Circulant Matrices and Cycles;Journal of Mathematics;2022-03-24