<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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 (𝒭)<sup>*</sup> = 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.</p></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.

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

Department of Mathematics, Science and Research Branch

Acta Universitatis Sapientiae, Mathematica

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...

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

Published Online: Dec 02, 2020

Page range: 358 - 369

Received: Feb 23, 2020

DOI: https://doi.org/10.2478/ausm-2020-0025

Keywords
metric dimension, strongly annihilating-ideal graph, commutative ring

© 2020 V. Soleymanivarniab et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Published Online: Dec 02, 2020

Page range: 358 - 369

Received: Feb 23, 2020

DOI: https://doi.org/10.2478/ausm-2020-0025

Keywordsmetric dimension, strongly annihilating-ideal graph, commutative ring

© 2020 V. Soleymanivarniab et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
metric dimension, strongly annihilating-ideal graph, commutative ring