Results 171 to 180 of about 2,362 (196)

ON THE ASSOCIATED GRAPHS TO A COMMUTATIVE RING

Journal of Algebra and Its Applications, 2012
Let R be a commutative ring with nonzero identity. For an arbitrary multiplicatively closed subset S of R, we associate a simple graph denoted by ΓS(R) with all elements of R as vertices, and two distinct vertices x, y ∈ R are adjacent if and only if x+y ∈ S. Two well-known graphs of this type are the total graph and the unit graph.
Barati, Z., Khashyarmanesh, K., Mohammadi, Fatemeh, Nafar, Khosro   +3 more
openaire   +2 more sources

Non-commuting graphs of rings

Discrete Mathematics, Algorithms and Applications, 2015
Let R be a non-commutative ring and let C(R) be the center of R. The non-commuting graph ΓR of R associated to R is defined as a graph with R\C(R) as the vertices and two distinct vertices x and y are joined whenever xy ≠ yx. We study various graph theoretical properties of this graph.
Abbas Erfanian, Kazem Khashyarmanesh, Kh. Nafar   +2 more
openaire   +2 more sources

THE JACOBSON GRAPH OF COMMUTATIVE RINGS

Journal of Algebra and Its Applications, 2012
Let R be a commutative ring with nonzero identity. Then the Jacobson graph of R, denoted by 𝔍R, is defined as a graph with vertex set R\J(R) such that two distinct vertices x and y are adjacent if and only if 1 - xy is not a unit of R. We obtain some graph theoretical properties of 𝔍R including its connectivity, planarity and perfectness and we ...
Azimi, A., Erfanian, A., Farrokhi D. G., M.   +2 more
openaire   +2 more sources

The unit graph of a commutative semiring

Summary: Let \(S\) be a commutative semiring with unity and \(U(S)\) be the set of all units of \(S\). The unit graph of \(S\), denoted by \(G(S)\), is the undirected graph with vertex set \(S\) and two distinct vertices \(x\) and \(y\) are adjacent if and only if \(x + y \in U(S)\). In this article, we have investigated some properties of unit graph \(
Boro, Laithun, Singh, Madan, Goswami, Jituparna   +2 more
openaire   +2 more sources

On the T-graph of a Commutative Ring

2012 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, 2012
Let R be a commutative ring with non-zero identity and let I be a proper ideal of R. In this talk we study the T-graph ΓIt(R) consisting of all elements of R as vertices, such that two vertices x and y in the graph are adjacent if and only if x + y ϵ S(I), where S(I) = {a ϵ R | ra ϵ, for somer ϵ R - I}.
openaire   +1 more source

ON THE COZERO-DIVISOR GRAPHS AND COMAXIMAL GRAPHS OF COMMUTATIVE RINGS

Journal of Algebra and Its Applications, 2012
Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R, denoted by Γ′(R), is a graph with vertices in W*(R), which is the set of all non-zero and non-unit elements of R, and two distinct vertices a and b in W*(R) are adjacent if and only if a ∉ bR and b ∉ aR.
Afkhami, Mojgan, Khashyarmanesh, Kazem
openaire   +2 more sources

On Laplacian Commutativity of Graphs

Malaysian Journal of Mathematical Sciences
This paper introduces the notion of Laplacian commutativity of graphs among well known classes of graphs. Two graphs are Laplacian commutative if their Laplacian matrices commute. The commutativity of the Laplacian matrix of a graph G with its complement, G′ , and its k− complement, GkP is also examined.
S. Nithya, P. Kuttipulackal
openaire   +1 more source

Between the enhanced power graph and the commuting graph

Journal of Graph Theory, 2023
Peter Cameron, Bojan Kuzma
exaly  

Commuting graph of a group action with few edges

Communications in Algebra, 2023
Gülin Ercan
exaly  

On the Structure of the Commuting Graph of Brandt Semigroups

Springer Proceedings in Mathematics and Statistics, 2021
Jitender Kumar, Sandeep Dalal, Kumar Jitender   +2 more
exaly