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

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

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.

Language: English
Page range: 358 - 369
Submitted on: Feb 23, 2020
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Published on: Dec 2, 2020
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 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.