Total graph of a module with respect to singular submodule

Goswami, Jituparna; Rajkhowa, Kukil Kalpa; Saikia, Helen K.

doi:10.1016/j.ajmsc.2015.10.002

Cited by 6 publications

(4 citation statements)

References 11 publications

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“…Many fundamental papers assigning graphs to rings and modules have appeared recently, for instance see, [1,2,4,7,19]. In 2008, Anderson and Badawi [3] have introduced the total graph of a commutative ring and later on this notion has been generalised to many algebraic structures, in particular to module over a commutative ring (see [10,11]).…”

Section: Introductionmentioning

confidence: 99%

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On domination in the total torsion element graph of a module

Goswami

Sarmah

2023

Proyecciones (Antofagasta)

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Let R be a commutative ring with non-zero unity and M be a unitary R-module. Let T(M) be the set of torsion elements of M. Atani and Habibi [6] introduced the total torsion element graph of M over R as an undirected graph T(Γ(M)) with vertex set as M and any two distinct vertices x and y are adjacent if and only if x + y ∈ T(M). The main objective of this paper is to study the domination properties of the graph T(Γ(M)). The domination number of T(Γ(M)) and its induced subgraphs T or(Γ(M)) and T of(Γ(M)) has been determined. Some domination parameters of T(Γ(M)) are also studied. In particular, the bondage number of T(Γ(M)) has been determined. Finally, it has been proved that T(Γ(M)) is excellent, domatically full and well covered under certain conditions.

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Section: Introductionmentioning

confidence: 99%

“…But not much research has been done on the domination parameters of graphs associated to algebraic structures such as groups, rings, modules in terms of algebraic properties. However, some works on domination of graphs associated to rings and modules have appeared recently, for instance see, [9,12,17,18,20,21].…”

Section: Introductionmentioning

confidence: 99%

On domination in the total torsion element graph of a module

Goswami

Sarmah

2023

Proyecciones (Antofagasta)

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“…Many fundamental papers assigning graphs to rings and modules have appeared recently, for instance see, [1, 3-5, 7, 19]. In 2008, Anderson and Badawi [4] have introduced the total graph of a commutative ring and later on this notion has been gen-eralised to many algebraic structures, in particular to module over a commutative ring (see [10,11]).…”

Section: Introductionmentioning

confidence: 99%

“…But not much research has been done on the domination parameters of graphs associated to algebraic structures such as groups, rings, modules in terms of alge-braic properties. However, some works on domination of graphs associated to rings and modules have appeared recently, for instance see, [9,16,18,20].…”

Section: Introductionmentioning

confidence: 99%

Domination in the entire nilpotent element graph of a module over a commutative ring

Goswami

Shabani

2021

Proyecciones (Antofagasta)

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Let R be a commutative ring with unity and M be a unitary R module. Let Nil(M) be the set of all nilpotent elements of M. The entire nilpotent element graph of M over R is an undirected graph E(G(M)) with vertex set as M and any two distinct vertices x and y are adjacent if and only if x + y ∈ Nil(M). In this paper we attempt to study the domination in the graph E(G(M)) and investigate the domination number as well as bondage number of E(G(M)) and its induced subgraphs N(G(M)) and Non(G(M)). Some domination parameters of E(G(M)) are also studied. It has been showed that E(G(M)) is excellent, domatically full and well covered under certain conditions.

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The rings of real numbers modulo n and complex numbers modulo n

Alhusiny

2023

International Conference of Computational Methods in Sciences and Engineering Iccmse 2021

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Total graph of a module with respect to singular submodule

Cited by 6 publications

References 11 publications

On domination in the total torsion element graph of a module

On domination in the total torsion element graph of a module

Domination in the entire nilpotent element graph of a module over a commutative ring

The rings of real numbers modulo n and complex numbers modulo n

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