Papers by Raoufeh Manaviyat
Journal of Mathematical Extension, Oct 22, 2014
A Steiner triple system of order v, STS(v), is an ordered pair S = (V, B), where V is a set of si... more A Steiner triple system of order v, STS(v), is an ordered pair S = (V, B), where V is a set of size v and B is a collection of triples of V such that every pair of V is contained in exactly one triple of B. A k-block coloring is a partitioning of the set B into k color classes such that every two blocks in one color class do not intersect. In this paper, we introduce a construction and use it to show that for every k-block colorable STS(v) and l-block colorable STS(w), there exists a (k+lv)-block colorable STS(vw). Moreover, it is shown that for every kblock colorable STS(v), every STS(2v+1) obtained from the well-known construction is (k + v)-block colorable.
Mediterranean Journal of Mathematics, 2015
The idempotent graph of a ring R, denoted by I(R), is a graph whose vertices are all nontrivial i... more The idempotent graph of a ring R, denoted by I(R), is a graph whose vertices are all nontrivial idempotents of R and two distinct vertices x and y are adjacent if and only if xy = yx = 0. In this paper, we show that diam$${(I(M_n(D))) = 4}$$(I(Mn(D)))=4, for all natural number $${n \geq 4}$$n≥4 and diam$${(I(M_3(D))) = 5}$$(I(M3(D)))=5, where D is a division ring. We also provide some classes of rings whose idempotent graphs are connected. Moreover, the regularity, clique number and chromatic number of idempotent graphs are studied.
Journal of Algebra Combinatorics Discrete Structures and Applications, May 15, 2018
The rings considered in this article are commutative with identity which admit at least two maxim... more The rings considered in this article are commutative with identity which admit at least two maximal ideals. Let R be a ring such that R admits at least two maximal ideals. Recall from Ye and Wu (J. Algebra Appl. 11(6): 1250114, 2012) that the comaximal ideal graph of R, denoted by C (R) is an undirected simple graph whose vertex set is the set of all proper ideals I of R such that I ⊆ J(R), where J(R) is the Jacobson radical of R and distinct vertices I1, I2 are joined by an edge in C (R) if and only if I1 + I2 = R.
Cornell University - arXiv, Jan 18, 2015
Let G be a graph and f : V (G) → N be a function. An f-coloring of a graph G is an edge coloring ... more Let G be a graph and f : V (G) → N be a function. An f-coloring of a graph G is an edge coloring such that each color appears at each vertex v ∈ V (G) at most f (v) times. The minimum number of colors needed to f-color G is called the f-chromatic index of G and is denoted by χ ′ f (G). It was shown that for every graph G, ∆ f (G) ≤ χ ′ f (G) ≤ ∆ f (G) + 1, where ∆ f (G) = max v∈V (G) ⌈ d G (v) f (v) ⌉. A graph G is said to be f-Class 1 if χ ′ f (G) = ∆ f (G), and f-Class 2, otherwise. Also, G∆ f is the induced subgraph of G on {v ∈ V (G) : d G (v) f (v) = ∆ f (G)}. In this paper, we show that if G is a connected graph with ∆(G∆ f) ≤ 2 and G has an edge cut of size at most ∆ f (G) − 2 which is a matching or a star, then G is f-Class 1. Also, we prove that if G is a connected graph and every connected component of G∆ f is a unicyclic graph or a tree and G∆ f is not 2-regular, then G is f-Class 1. Moreover, we show that except one graph, every connected claw-free graph G whose f-core is 2-regular with a vertex v such that f (v) = 1 is f-Class 1.
Iranian Journal of Science and Technology, Transactions A: Science, 2017
Let R be a ring, S a strictly ordered monoid, and x : S ! EndðRÞ a monoid homomorphism. The skew ... more Let R be a ring, S a strictly ordered monoid, and x : S ! EndðRÞ a monoid homomorphism. The skew generalized power series ring R[[S, x]] is a common generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomial rings, (skew) group rings, and Malcev-Neumann Laurent series rings. In the current work, we study the (S, x)-nil Armendariz condition on R, a generalization of the standard nil-Armendariz condition from polynomials and power series to skew generalized power series. We resolve the structure of (S, x)-nil Armendariz rings and obtain various necessary or sufficient conditions for a ring to be (S, x)-nil Armendariz, unifying and generalizing a number of known nil Armendariz-like conditions in the aforementioned special cases. For example, we show that left uniserial nilpotent semicommutative rings are nil Armendariz. Moreover, we study on the relationship between the zip and weak zip properties of a ring R and these of the ring R[[S, x]].
Journal of Algebra and Its Applications, 2013
Let R be a ring, M a monoid and ω : M → End (R) a monoid homomorphism. The skew monoid ring R * M... more Let R be a ring, M a monoid and ω : M → End (R) a monoid homomorphism. The skew monoid ring R * M is a common generalization of polynomial rings, skew polynomial rings, (skew) Laurent polynomial rings and monoid rings. In the current work, we study the nil skew M-Armendariz condition on R, a generalization of the standard nil-Armendariz condition from polynomials to skew monoid rings. We resolve the structure of nil skew M-Armendariz rings and obtain various necessary or sufficient conditions for a ring to be nil skew M-Armendariz, unifying and generalizing a number of known nil Armendariz-like conditions in the aforementioned special cases. We consider central idempotents which are invariant under a monoid endomorphism of nil skew M-Armendariz rings and classify how the nil skew M-Armendariz rings behaves under various ring extensions. We also provide rich classes of skew monoid rings which satisfy in a condition nil (R * M) = nil (R) * M. Moreover, we study on the relationship bet...
Journal of Algebra and Its Applications, 2013
The idempotent graph of a ring R, denoted by I(R), is a graph whose vertices are all nontrivial i... more The idempotent graph of a ring R, denoted by I(R), is a graph whose vertices are all nontrivial idempotents of R and two distinct vertices x and y are adjacent if and only if xy = yx = 0. In this paper we show if D is a division ring, then the clique number of I(Mn(D))(n ≥ 2) is n and for any commutative Artinian ring R the clique number and the chromatic number of I(R) are equal to the number of maximal ideals of R. We prove that for every left Noetherian ring R, the clique number of I(R) is finite. For every finite field F, we also determine an independent set of I(Mn(F)) with maximum size. If F is an infinite field, then we prove that the domination number of I(Mn(F)) is infinite. We show that the idempotent graph of every reduced ring is connected and if n ≥ 3 and D is a division ring, then I(Mn(D)) is connected and moreover diam(I(Mn(D))) ≤ 5.
Graphs and Combinatorics, 2011
Suppose that G is a graph and f : V (G) → N is a labeling of the vertices of G. Let S(v) denote t... more Suppose that G is a graph and f : V (G) → N is a labeling of the vertices of G. Let S(v) denote the sum of labels over all neighbors of the vertex v in G. A labeling f of G is called lucky if S(u) = S(v), for every pair of adjacent vertices u and v. Also, for each vertex v ∈ V (G), let L(v) denote a list of natural numbers available at v. A list lucky labeling, is a lucky labeling f such that f (v) ∈ L(v), for each v ∈ V (G). A graph G is said to be lucky k-choosable if every k-list assignment of natural numbers to the vertices of G permits a list lucky labeling of G. The lucky choice number of G, η l (G), is the minimum natural number k such that G is lucky k-choosable. In this paper, we prove that for every graph G with ≥ 2, η l (G) ≤ 2 − + 1, where denotes the maximum degree of G. Among other results we show that for every 3-list assignment to the vertices of a forest, there is a list lucky labeling which is a proper vertex coloring too.
Electronic Notes in Discrete Mathematics, 2014
The inclusion ideal graph of a ring R, denoted by In(R), is a graph whose vertices are all non-tr... more The inclusion ideal graph of a ring R, denoted by In(R), is a graph whose vertices are all non-trivial left ideals of R and two distinct left ideals I and J are adjacent if and only if I ⊆ J or J ⊆ I. In this paper, we show that In(R) is not connected if and only if R ∼ = M 2 (D) or D 1 × D 2 , for some division rings
Communications in Algebra, 2010
Let α be an endomorphism of R which is not assumed to be surjective and R be α-compatible. It is ... more Let α be an endomorphism of R which is not assumed to be surjective and R be α-compatible. It is shown that the skew power series ring R[[x; α]] is right p.q.-Baer if and only if the skew Laurent series ring R[[x, x ; α]] is right p.q.-Baer if and only if R is right p.q.-Baer and every countable subset
Communications in Algebra, 2010
ABSTRACT A ring R with an automorphism α and an α-derivation δ is called (α,δ)-quasi-Baer (resp.,... more ABSTRACT A ring R with an automorphism α and an α-derivation δ is called (α,δ)-quasi-Baer (resp., quasi-Baer) if the right annihilator of every (α,δ)-ideal (resp. ideal) of R is generated by an idempotent, as a right ideal. We show the left-right symmetry of (α, δ)-quasi Baer condition and prove that a ring R is (α, δ)-quasi Baer if and only if R[x; α, δ] is α-quasi Baer if and only if R[x; α, δ] is -quasi Baer for every extended derivation of δ. When R is a ring with IFP, then R is (α, δ)-Baer if and only if R[x; α, δ] is α-Baer if and only if R[x; α, δ] is -Baer for every extended α-derivation on R[x; α, δ] of δ. A rich source of examples for (α, δ)-quasi Baer rings is provided.
Communications in Algebra, 2012
We study the skew inverse Laurent-serieswise Armendariz (or simply, SIL-Armendariz) condition on ... more We study the skew inverse Laurent-serieswise Armendariz (or simply, SIL-Armendariz) condition on R, a generalization of the standard Armendariz condition from polynomials to skew inverse Laurent series. We study relations between the set of annihilators in R and the set of annihilators in R((x ; α)). Among applications, we show that a number of interesting properties of a SIL-Armendariz ring
Communications in Algebra, 2012
ABSTRACT For a ring R with a derivation δ, we introduce and investigate a generalization of reduc... more ABSTRACT For a ring R with a derivation δ, we introduce and investigate a generalization of reduced rings which we call an Armendariz ring of pseudo-differential operator type (or simply DO-Armendariz ring). Various classes of non-reduced DO-Armendariz rings is provided and a number of properties of this generalization are established. Radicals of the pseudo-differential operator ring R((x -1, δ)), in terms of those of a DO-Armendariz ring R, is established.
Australas. J Comb., 2019
Let G be a graph and f : V (G) → N be a function. An f -coloring of a graph G is an edge coloring... more Let G be a graph and f : V (G) → N be a function. An f -coloring of a graph G is an edge coloring such that each color appears at each vertex v ∈ V (G) at most f(v) times. The minimum number of colors needed to f -color G is called the f -chromatic index of G and is denoted by χf (G). It was shown that for every graph G, Δf(G) ≤ χf(G) ≤ Δf (G) + 1, where Δf (G) = maxv∈V (G) dG(v) f(v) . A graph G is said to be f -Class 1 ISSN: 2202-3518 c ©The author(s). Released under the CC BY 4.0 International License S. AKBARI ET AL. /AUSTRALAS. J. COMBIN. 75 (1) (2019), 32–49 33 if χf (G) = Δf(G), and f -Class 2, otherwise. Also, GΔf is the induced subgraph of G on {v ∈ V (G) : dG(v) f(v) = Δf (G)}. In this paper, we show that if G is a connected graph with Δ(GΔf ) ≤ 2 and G has an edge cut of size at most Δf(G)− 2 which is a star, then G is f -Class 1. Also, we prove that if G is a connected graph and every connected component of GΔf is a unicyclic graph or a tree and GΔf is not 2-regular, the...
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 d... more 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 Γ2(R) is the subgraph of Γ(R) induced by the non-unit elements.
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Papers by Raoufeh Manaviyat