Intersection graphs of ideals of rings

Chakrabarty, Ivy; Ghosh, Suparna; Mukherjee, Tilottama; Sen, M. K.

doi:10.1016/j.disc.2008.11.034

Cited by 140 publications

(73 citation statements)

References 6 publications

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“…Intersection graph was first introduced by Bosak in 1965 for semigroup see [7], defined as vertices are the sub semigroups of that semigroup and in which two distinct vertices are adjacent if they have non trivial intersection. Many researchers worked on these intersection graphs by considering the members of F have different algebraic structures and in which those see [8,9,17]. In [16], the intersection graph G Z (R) of zero-divisors of a finite commutative ring R is a simple undirected graph whose vertices are the nonzero zero-divisors of R and in which two distinct vertices x and y are adjacent if and only if their corresponding principal ideals having nonzero intersection.…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian property of intersection graph of zero divisors of the ring Zn

Sajana¹,

Bharathi²

2018

Malaya J. Mat.

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The intersection graph G Z (Z n ) of zero-divisors of the ring Z n , the ring of integers modulo n is a simple undirected graph with the vertex set is Z(Z n ) * = Z(Z n ) \ {0}, the set of all nonzero zero-divisors of the ring Z n and for any two distinct vertices are adjacent if and only if their corresponding principal ideals have a nonzero intersection. We determine some results concerning the necessary and sufficient condition for the graph G Z (Z n ) is Hamiltonian. Also, we investigate for all values of for which the graph G Z (Z n ) is Hamiltonian and as an example we show that how the results give as easy proof of the existence of a Hamilton cycle.

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Section: Introductionmentioning

confidence: 99%

Hamiltonian property of intersection graph of zero divisors of the ring Zn

Sajana¹,

Bharathi²

2018

Malaya J. Mat.

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“…Various construction of graphs relative to the ring structure are found in Simis et al (1994). Chakrabarty et al (2009) studied the intersection graphs of ideal of rings. They determined the values of n for which G(Z n ) for ring Z n of integers modulo n for n∈N is connected, complete, bipartite, Eulerian and Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

A Kind of Intersection Graphs on Ideals of a Ring

Talebi¹

2012

Journal of Mathematics and Statistics

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“…Several other classes of graphs associated with algebraic structures have been also actively investigated. For example, see [1], [3], [5], [6], [12] and [13].…”

Section: Introductionmentioning

confidence: 99%

Generalized Cayley Graph of Upper Triangular Matrix Rings

Afkhami¹,

Hashemifar²,

Khashyarmanesh³

2016

Bulletin of the Korean Mathematical Society

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Abstract. Let R be a commutative ring with the non-zero identity and n be a natural number. Γ n R is a simple graph with R n \ {0} as the vertex set and two distinct vertices X and Y in R n are 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 such that AX t = Y t or AY t = X t , where, for a matrix B, B t is the matrix transpose of B. Γ n R is a generalization of Cayley graph. Let Tn(R) denote the n × n upper triangular matrix ring over R. In this paper, for an arbitrary ring R, we investigate the properties of the graph Γ n Tn (R) .

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Intersection graphs of ideals of rings

Cited by 140 publications

References 6 publications

Hamiltonian property of intersection graph of zero divisors of the ring Zn

Hamiltonian property of intersection graph of zero divisors of the ring Zn

A Kind of Intersection Graphs on Ideals of a Ring

Generalized Cayley Graph of Upper Triangular Matrix Rings

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