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

V. Soleymanivarniab

V. Soleymanivarniab

Department of Mathematics, Science and Research Branch, Islamic Azad University (IAU)Tehran,
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Soleymanivarniab, V.
, 
R. Nikandish

R. Nikandish

Department of Mathematics, Jundi-Shapur University of TechnologyDezful,
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Nikandish, R.
 and 
A. Tehranian

A. Tehranian

Department of Mathematics, Science and Research Branch, Islamic Azad University (IAU)Tehran,
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Tehranian, A.
  
Dec 02, 2020
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Published Online: Dec 02, 2020
Page range: 358 - 369
Received: Feb 23, 2020
DOI: https://doi.org/10.2478/ausm-2020-0025
Keywords
© 2020 V. Soleymanivarniab et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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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English
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Journal Subjects:
Mathematics, General Mathematics
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