SARMAN PATAT | Saurashtra University, Rajkot (original) (raw)

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Papers by SARMAN PATAT

Research paper thumbnail of 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.

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

Malaya Journal of Matematik, 2020

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.

Research paper thumbnail of 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.

Research paper thumbnail of 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.

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

Malaya Journal of Matematik, 2020

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.

Research paper thumbnail of 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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