Results 11 to 20 of about 1,060 (95)

An Algebraic Approach of Topological Indices Connected with Finite Quasigroups

Journal of Function Spaces
In mathematical chemistry, the algebraic polynomial serves as essential for calculating the most accurate expressions of distance-based, degree-distance-based, and degree-based topological indices.
Muhammad Nadeem, Md. Ashraful Alam, Nwazish Ali, M. I. Elashiry   +3 more
doaj   +2 more sources

Linking Bipartiteness and Inversion in Algebra via Graph-Theoretic Methods and Simulink

Complexity
Research for decades has concentrated on graphs of algebraic structures, which integrate algebra and combinatorics in an innovative way. The goal of this study is to characterize specific aspects of bipartite and inverse graphs that are associated with ...
Mohammad Mazyad Hazzazi, Muhammad Nadeem, Muhammad Kamran, Muhammad Arshad, M. I. Elashiry, Samuel Asefa Fufa   +5 more
doaj   +2 more sources

Quantum quasigroups and loops

Journal of Algebra, 2016
A quantum quasigroup is a family \((A,\nabla,\Delta)\), where \((A,\nabla)\) is a magma in a given symmetric monoidal category, \((A,\Delta)\) is a comagma in the same category, such that the compositions \((\Delta\otimes 1_A)\circ(1_A\otimes\nabla)\) and \((1_A\otimes\Delta)(\nabla\otimes 1_A)\) are invertible.
Jonathan Smith; Jdh Smith; Jonathan Dh Smith
openaire   +4 more sources

Rectangular quasigroups and rectangular loops

Computers & Mathematics with Applications, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kinyon, M.K., Phillips, J.D.
openaire   +3 more sources

Principal Loop-Isotopes of Quasigroups [PDF]

Canadian Journal of Mathematics, 1966
If a quasigroup (L, .) has finite order n, then there are n2 principal loop-isotopes. Some of these n2 loops may be isomorphic, and the main purpose of this paper is to obtain theorems that describe the isomorphism classes. Using these results and a computer, we have determined all the loops of order 6.
Bryant, B. F., Schneider, H.
openaire   +1 more source

Small latin squares, quasigroups, and loops [PDF]

Journal of Combinatorial Designs, 2006
AbstractWe present the numbers of isotopy classes and main classes of Latin squares, and the numbers of isomorphism classes of quasigroups and loops, up to order 10. The best previous results were for Latin squares of order 8 (Kolesova, Lam, and Thiel,1990), quasigroups of order 6 (Bower,2000), and loops of order 7 (Brant and Mullen,1985). The loops of
McKay, Brendan, Meynert, Alison, Myrvold, Wendy   +2 more
openaire   +3 more sources

A New Graphical Representation of the Old Algebraic Structure

Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023
The most recent advancements in algebra and graph theory enable us to ask a straightforward question: what practical use does this graph connected with a mathematical system have in the real world? With the use of algebraic approaches, we may now tackle a wide range of graph theory‐related problems.
Muhammad Nadeem, Imran Siddique, Md. Ashraful Alam, Waqas Ali, Xuanlong Ma   +4 more
wiley   +1 more source

Some Algebraic Properties of the Wilson Loop

Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022
In this article, some algebraic properties of the Wilson loop have been investigated in a broad manner. These properties include identities, autotopisms, and implications. We use some equivalent conditions to study the behavior of holomorphism of this loop. Under the shadow of this holomorphism, we are able to observe coincident loops.
Han Li, M. Nadeem, M. A. Ali, H. Mutee ur Rehman, Yuan Yi   +4 more
wiley   +1 more source

[Retracted] Double Weak Hopf Quiver and Its Path Coalgebra

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
The main input of this research is the introduction of the concept of double weak Hopf quiver (DWHQ). In addition, the structures of weak Hopf algebra (WHA) are obtained through path coalgebra of the proposed quivers. Furthermore, the module and comodule structures on the said WHA are discussed.
Muhammad Naseer Khan, Munir Ahmed, Muhammad Arshad, Waleed Almutiry, Rashad A. R. Bantan, Mohammed Elgarhy, Muhammad Gulzar   +6 more
wiley   +1 more source

On Characterization of Graphs Structures Connected with Some Algebraic Properties

Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022
In this paper, we have characterized graph structures connected with some algebraic properties. Also, this paper is actually the concatenation of graph theory and algebra. We have introduced left and right inverse graphs of antiautomorphic inverse property loops.
Rongbing Huang, Muhammad Nadeem, Iqra Rashid, M.K. Siddiqui, Samuel Asefa Fufa, Shaojian Qu   +5 more
wiley   +1 more source