Results 31 to 40 of about 2,044 (191)

A Note on Comaximal Graph of Non-commutative Rings [PDF]

Algebras and Representation Theory, 2011
Let $R$ be a ring with unity. The graph $Γ(R)$ is a graph with vertices as elements of $R$, where two distinct vertices $a$ and $b$ are adjacent if and only if $Ra+Rb=R$. Let $Γ_2(R)$ is the subgraph of $Γ(R)$ induced by the non-unit elements. H.R. Maimani et al. [H.R. Maimani et al., Comaximal graph of commutative rings, J.
Akbari, Saieed, Habibi, Mohammad, Majidinya, Ali, Manaviyat, Raoofe   +3 more
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Graphs defined on groups [PDF]

International Journal of Group Theory, 2022
‎This paper concerns aspects of various graphs whose vertex set is a group $G$‎ ‎and whose edges reflect group structure in some way (so that‎, ‎in particular‎, ‎they are invariant under the action of the automorphism group of $G$)‎.
Peter J‎. Cameron
doaj   +1 more source

On the Unit Graph of a Non-commutative Ring [PDF]

Algebra Colloquium, 2015
Let R be a ring with non-zero identity. The unit graph G(R) of R is a graph with elements of R as its vertices and two distinct vertices a and b are adjacent if and only if a + b is a unit element of R. It was proved that if R is a commutative ring and 𝔪 is a maximal ideal of R such that |R/𝔪| = 2, then G(R) is a complete bipartite graph if and only ...
Akbari, S., Estaji, E., Khorsandi, M. R.
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On the Spectra of Commuting and Non Commuting Graph on Dihedral Group

Cauchy: Jurnal Matematika Murni dan Aplikasi, 2017
Study about spectra of graph has became interesting work as well as study about commuting and non commuting graph of a group or a ring. But the study about spectra of commuting and non commuting graph of dihedral group has not been done yet.
Abdussakir Abdussakir, Rivatul Ridho Elvierayani, Muflihatun Nafisah   +2 more
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A combinatorial non-commutative Hopf algebra of graphs [PDF]

Discrete Mathematics & Theoretical Computer Science, 2014
Combinatorics A non-commutative, planar, Hopf algebra of planar rooted trees was defined independently by one of the authors in Foissy (2002) and by R. Holtkamp in Holtkamp (2003). In this paper we propose such a non-commutative Hopf algebra for graphs. In order to define a non-commutative product we use a quantum field theoretical (QFT) idea,
Duchamp, Gerard, Foissy, Loïc, Hoang-Nghia, Nguyen, Manchon, Dominique, Tanasa, Adrian   +4 more
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On Generalized Non-commuting Graph of a Finite Ring [PDF]

Algebra Colloquium, 2018
Let S and K be two subrings of a finite ring R. Then the generalized non-commuting graph of subrings S, K of R, denoted by ГS,K, is a simple graph whose vertex set is [Formula: see text], and where two distinct vertices a, b are adjacent if and only if [Formula: see text] or [Formula: see text] and [Formula: see text].
Dutta, Jutirekha, Basnet, Dhiren Kumar, Nath, Rajat Kanti   +2 more
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Non-commuting graph of the dihedral group determined by Hosoya parameters

Alexandria Engineering Journal, 2022
Hosoya introduced the concept of graph terminologies in chemistry and provide a modeling for molecules. This modeling leads to predict the chemical properties of molecules, easy classification of chemical compounds, computer simulations and computer ...
Muhammad Salman, Tahira Noreen, Masood Ur Rehman, Jinde Cao, Muhammad Zafar Abbas   +4 more
doaj   +1 more source

Sandwich theorems and capacity bounds for non-commutative graphs [PDF]

Journal of Combinatorial Theory, Series A, 2021
We define non-commutative versions of the vertex packing polytope, the theta convex body and the fractional vertex packing polytope of a graph, and establish a quantum version of the Sandwich Theorem of Grötschel, Lovász and Schrijver. We define new non-commutative versions of the Lovász number of a graph which lead to an upper bound of the zero-error ...
Gareth Boreland, Ivan G. Todorov, Andreas J. Winter 0002   +2 more
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GENUS OF COMMUTING GRAPHS OF CERTAIN FINITE GROUPS [PDF]

Journal of Algebraic Systems
The commuting graph of a finite group G is a graph whose vertex set is the set of non-central elements of G and two distinct vertices are adjacent if they commute.
Parhajit Bhowal, Rajat Nath
doaj   +1 more source

Quantum State Assignment Flows

Entropy, 2023
This paper introduces assignment flows for density matrices as state spaces for representation and analysis of data associated with vertices of an underlying weighted graph.
Jonathan Schwarz, Jonas Cassel, Bastian Boll, Martin Gärttner, Peter Albers, Christoph Schnörr   +5 more
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