Diameter and girth of Torsion Graph

P. Malakooti Rad; S. Yassemi; Sh. Ghalandarzadeh; P. Safari

doi:10.2478/auom-2014-0054

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Diameter and girth of Torsion Graph

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 22 (2014): Issue 3 (September 2014)

By: P. Malakooti Rad, S. Yassemi, Sh. Ghalandarzadeh and P. Safari

Open Access

|Dec 2015

Abstract

Let R be a commutative ring with identity. Let M be an R-module and T (M)* be the set of nonzero torsion elements. The set T(M)* makes up the vertices of the corresponding torsion graph, Γ_R(M), with two distinct vertices x, y ∈ T(M)* forming an edge if Ann(x) ∩ Ann(y) ≠ 0. In this paper we study the case where the graph Γ_R(M) is connected with diam(Γ_R(M)) ≤ 3 and we investigate the relationship between the diameters of Γ_R(M) and Γ_R(R). Also we study girth of Γ_R(M), it is shown that if Γ_R(M) contains a cycle, then gr(Γ_R(M)) = 3.

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Articles in this issue

DOI: https://doi.org/10.2478/auom-2014-0054 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 127 - 136

Submitted on: Jun 12, 2013

Accepted on: Sep 24, 2013

Published on: Dec 22, 2015

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Diameter,

Girth,

Multiplication modules,

Torsion graphs

Related subjects:

Mathematics,

General mathematics

© 2015 P. Malakooti Rad, S. Yassemi, Sh. Ghalandarzadeh, P. Safari, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 22 (2014): Issue 3 (September 2014)