On the metric dimension of strongly annihilating-ideal graphs of commutative rings

V. Soleymanivarniab; R. Nikandish; A. Tehranian

doi:10.2478/ausm-2020-0025

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On the metric dimension of strongly annihilating-ideal graphs of commutative rings

Acta Universitatis Sapientiae, Mathematica

Volume 12 (2020): Issue 2 (November 2020)

By: V. Soleymanivarniab, R. Nikandish and A. Tehranian

Open Access

|Dec 2020

Abstract

Let 𝒭 be a commutative ring with identity and 𝒜(𝒭) be the set of ideals with non-zero annihilator. The strongly annihilating-ideal graph of 𝒭 is defined as the graph SAG(𝒭) with the vertex set 𝒜 (𝒭)^* = 𝒜 (𝒭) \{0} and two distinct vertices I and J are adjacent if and only if I ∩ Ann(J) ≠ (0) and J ∩ Ann(I) ≠ (0). In this paper, we study the metric dimension of SAG(𝒭) and some metric dimension formulae for strongly annihilating-ideal graphs are given.

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Articles in this issue

DOI: https://doi.org/10.2478/ausm-2020-0025 | Journal eISSN: 2066-7752

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Language: English

Page range: 358 - 369

Submitted on: Feb 23, 2020

Published online: Dec 2, 2020

Published in print: Nov 1, 2020

Published by: Sapientia Hungarian University of Transylvania

In partnership with: Paradigm Publishing Services

Keywords:

metric dimension,

strongly annihilating-ideal graph,

commutative ring

MSC:

13A99,

05C78,

05C12

Related subjects:

Mathematics,

General mathematics

© 2020 V. Soleymanivarniab, R. Nikandish, A. Tehranian, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 12 (2020): Issue 2 (November 2020)