Mojgan Afkhami

TL;DR: In this paper, all finite groups whose commuting (noncommuting) graphs can be embed on the plane, torus, or projective plane are classified, and all of them can be found on the Euclidean plane.

TL;DR: In this article, a simple Cayley graph, denoted by Γ R n, with R n ⧹ { 0 } as the vertex set and two distinct vertices X and Y in R n being adjacent if and only if there exists an n × n lower triangular matrix A over R whose entries on the main diagonal are non-zero and such that AX T = Y T or AY T = X T, where, for a matrix B, B T is the matrix transpose of B.

TL;DR: In this article, the authors characterize all finite commutative rings R such that Γ′(R) is planar, outerplanar or ring graph, and show that all of them are planar.

TL;DR: In this paper, the authors associate a graph G∗(P) to a partially ordered set (poset, briefly) with the least element 0, as an undirected graph with vertex set P∗=P∖{0}.

TL;DR: In this article, the concept of the cozero-divisor graph was extended to any arbitrary ring with nonzero identity and some basic properties of this graph were studied. And some results on the co-zero-Divisor graphs of matrix rings were obtained.