On domination in the total torsion element graph of a module

Authors

  • Jituparna Goswami Gauhati University,
  • Moytri Sarmah Girijananda Chowdhury Institute of Management and Technology.

DOI:

https://doi.org/10.22199/issn.0717-6279-4904

Keywords:

bondage number, domination number, total torsion element graph, torsion elements; non-torsion elements

Abstract

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.

Author Biographies

Jituparna Goswami, Gauhati University,

Department of Mathematics.

Moytri Sarmah, Girijananda Chowdhury Institute of Management and Technology.

Department of Mathematics.

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Published

2023-05-16

How to Cite

[1]
J. Goswami and M. Sarmah, “On domination in the total torsion element graph of a module”, Proyecciones (Antofagasta, On line), vol. 42, no. 3, pp. 795-814, May 2023.

Issue

Vol. 42 No. 3 (2023)

Section

Artículos

Copyright (c) 2023 Jituparna Goswami, Moytri Sarmah

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