pravin vadhel

Gujarat Technological University, Applied Science and Humanities, Faculty Member

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I Pravin Vadhel Working as an Assistant Professor in Mathematics at V.V.P. Engineering College, Rajkot-05. My Qualification is M.Sc., M.Phil,.B.Ed., NET(CSIR HRD UGC), GSET, Ph.D.(thesis submitted) in MATHEMATICS. I like MATHEMATICS subject most and enjoying it lot. I like to learn new topics in MATHEMATICS.

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pravin vadhel

Mojgan Afkhami

Journal of Algebra Combinatorics Discrete Structures and Applications

Tamizh Chelvam T

Manonmaniam Sundaranar University

Asir Jacob

GIN RAS, MSU, alumnus

Dr. T. Tamizh Chelvam

hamidreza maimani

kazem khashyarmanesh

Selvakumar krishnan

Manonmaniam Sundaranar University, Tamilnadu, India

jafar amjadi

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Planarity of a unit graph: Part -II $ |Max(R)| = 2 $ case

The rings considered in this article are commutative with identity 1 6= 0. Recall that the unit g... more The rings considered in this article are commutative with identity 1 6= 0. Recall that the unit graph of a ring R is a simple undirected graph whose vertex set is the set of all elements of the ring R and two distinct vertices x,y are adjacent in this graph if and only if x+ y ∈U(R) where U(R) is the set of all unit elements of ring R. We denote this graph by UG(R). In this article we classified rings R with |Max(R)|= 2 such that UG(R) is planar.

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Planarity of a unit graph: Part-I local case

The rings considered in this article are commutative with identity 1 6= 0. Recall that the unit g... more The rings considered in this article are commutative with identity 1 6= 0. Recall that the unit graph of a ring R is a simple undirected graph whose vertex set is the set of all elements of the ring R and two distinct vertices x,y are adjacent in this graph if and only if x+ y ∈U(R) where U(R) is the set of unit elements of ring R. We denote this graph by UG(R). In this article we classified local ring R such that UG(R) is planar.

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Some results on a spanning subgraph of the intersection graph of ideals of a commutative ring

The rings considered in this article are commutative with identity and which admit at least one n... more The rings considered in this article are commutative with identity and which admit at least one nonzero proper ideal. For a ring R, we denote by I(R), the set of all proper ideals of R and let I(R)∗ = I(R)\{(0)}. In this article, for any ring R, we associate an undirected simple graph, denoted by H(R), whose vertex set is I(R)∗ and distinct vertices I, J are joined by an edge in this graph if and only if IJ 6= (0). For a ring R, we determine necessary and sufficient conditions in order that H(R) is connected and also find its diameter when it is connected. We prove that girth(H(R)) is either equal to 3 or ∞. Moreover, we classify the rings R for which girth(H(R)) = 3. Furthermore, we determine necessary and sufficient conditions in order that H(R) is complemented.

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On the dominating sets of the complement of the annihilating ideal graph of a commutative ring

Let R be a commutative ring with identity which is not an integral domain. Let A(R)∗ denote the c... more Let R be a commutative ring with identity which is not an integral domain. Let A(R)∗ denote the collection of all nonzero annihilating ideals of R and AG(R) denote the annihilating ideal graph of R. In this article, we consider the dominating sets of (AG(R))c (where (AG(R))c is the complement of AG(R)) and study the influence of the dominating sets of (AG(R))c on the ring structure of R and vice-versa.

Some Results on Intersection Graphs of Ideals of Commutative Rings

The rings considered in this article are commutative with identity which admit at least one nonze... more The rings considered in this article are commutative with identity which admit at least one nonzero proper ideal. Let R be a ring. Recall that the intersection graph of ideals of R, denoted by G(R), is an undirected simple graph whose vertex set is the set of all nontrivial ideals of R (an ideal I of R is said to be nontrivial if I / ∈ {(0), R}) and distinct vertices I, J are joined by an edge in G(R) if and only if I ∩ J 6= (0). Let r ∈ N. The aim of this article is to characterize rings R such that G(R) is either bipartite or 3-partite. MSC: 13A15.

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$Research paper thumbnail of Planarity of a unit graph part -III $ |Max(R)| \geq 3 $ case$

Planarity of a unit graph part -III $ |Max(R)| \geq 3 $ case

Malaya Journal of Matematik

The rings considered in this article are commutative with identity 1 = 0. Recall that the unit gr... more The rings considered in this article are commutative with identity 1 = 0. Recall that the unit graph of a ring R is a simple undirected graph whose vertex set is the set of all elements of the ring R and two distinct vertices x, y are adjacent in this graph if and only if x + y ∈ U(R) where U(R) is the set of all unit elements of ring R. We denote this graph by UG(R). In this article we classified rings R with |Max(R)| ≥ 3 such that UG(R) is planar.

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Algebra and Discrete Mathematics Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring I, nonquasilocal case

A b s t r ac t . The rings considered in this article are nonzero commutative with identity which... more A b s t r ac t . The rings considered in this article are nonzero commutative with identity which are not fields. Let R be a ring. We denote the collection of all proper ideals of R by I(R) and the collection I(R)\{(0)} by I(R) * . Recall that the intersection graph of ideals of R, denoted by G(R), is an undirected graph whose vertex set is I(R) * and distinct vertices I, J are adjacent if and only if I ∩ J = (0). In this article, we consider a subgraph of G(R), denoted by H(R), whose vertex set is I(R) * and distinct vertices I, J are adjacent in H(R) if and only if IJ = (0). The purpose of this article is to characterize rings R with at least two maximal ideals such that H(R) is planar.

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Planarity of a unit graph: Part -II $ |Max(R)| = 2 $ case

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Planarity of a unit graph: Part-I local case

The rings considered in this article are commutative with identity 1 6= 0. Recall that the unit g... more The rings considered in this article are commutative with identity 1 6= 0. Recall that the unit graph of a ring R is a simple undirected graph whose vertex set is the set of all elements of the ring R and two distinct vertices x,y are adjacent in this graph if and only if x+ y ∈U(R) where U(R) is the set of unit elements of ring R. We denote this graph by UG(R). In this article we classified local ring R such that UG(R) is planar.

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Some results on a spanning subgraph of the intersection graph of ideals of a commutative ring

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On the dominating sets of the complement of the annihilating ideal graph of a commutative ring

Some Results on Intersection Graphs of Ideals of Commutative Rings

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$Research paper thumbnail of Planarity of a unit graph part -III $ |Max(R)| \geq 3 $ case$

Planarity of a unit graph part -III $ |Max(R)| \geq 3 $ case

Malaya Journal of Matematik

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Algebra and Discrete Mathematics Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring I, nonquasilocal case

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