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K. Selvakumar

Bio: K. Selvakumar is an academic researcher from Manonmaniam Sundaranar University. The author has contributed to research in topics: Commutative ring & Mathematics. The author has an hindex of 4, co-authored 18 publications receiving 72 citations.

Papers
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Journal ArticleDOI
TL;DR: All finite commutative non-local rings R for which the k -zero-divisor hypergraph is planar are characterized.

16 citations

Journal ArticleDOI
TL;DR: In this article , the authors derived a formula for the Wiener index of the zero-divisor graph Γ (R ) for R = Z n , the ring of integers modulo n.

11 citations

Journal ArticleDOI
TL;DR: This paper investigates the interplay between the graph theoretic properties of IΓ(R) and the ring theoretics properties of R and study about various properties of the graph.
Abstract: Let R be a commutative ring. The intersection graph of gamma sets in the zero-divisor graph Γ(R) of R is the graph IΓ(R) with vertex set as the collection of all gamma sets of the zero-divisor graph Γ(R) of R and two distinct vertices A and B are adjacent if and only if A ∩ B ≠ ∅. In this paper, we study about various properties of IΓ(R) and investigate the interplay between the graph theoretic properties of IΓ(R) and the ring theoretic properties of R.

6 citations

Journal ArticleDOI
TL;DR: This paper extends the concept of the annihilating-ideal graph of a commutative ring to the hypergraph for which an algebraic ring is defined, and defines angebraic ring for which the graph is an annihilating graph.

5 citations


Cited by
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Journal ArticleDOI

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08 Dec 2001-BMJ
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

33,785 citations

Book ChapterDOI
01 Jan 1994
TL;DR: For the list object, introduced in Chapter 5, it was shown that each data element contains at most one predecessor element and one successor element, so for any given data element or node in the list structure, the authors can talk in terms of a next element and a previous element.
Abstract: For the list object, introduced in Chapter 5, it was shown that each data element contains at most one predecessor element and one successor element. Therefore, for any given data element or node in the list structure, we can talk in terms of a next element and a previous element.

381 citations

Journal ArticleDOI
01 Jan 1975

71 citations

Journal ArticleDOI
TL;DR: The k-zero-divisor hypergraph of R, denoted by ℋk(R), is a hypergraph with vertex vertices as discussed by the authors, where k is a constant.
Abstract: Let R be a commutative ring with identity and let Z(R,k) be the set of all k-zero-divisors in R and k>2 an integer. The k-zero-divisor hypergraph of R, denoted by ℋk(R), is a hypergraph with vertex...

15 citations