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THE METRIC DIMENSION OF THE ANNIHILATING-IDEAL GRAPH OF A FINITE COMMUTATIVE RING

Part of: Chain conditions, growth conditions, and other forms of finiteness Arithmetic rings and other special rings Graph theory

Published online by Cambridge University Press:  27 April 2021

DAVID DOLŽAN Open the ORCID record for DAVID DOLŽAN [Opens in a new window]
DAVID DOLŽAN*
Affiliation:
Department of Mathematics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 21, SI-1000Ljubljana, Slovenia
*
e-mail: [email protected]
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Abstract

We determine the metric dimension of the annihilating-ideal graph of a local finite commutative principal ring and a finite commutative principal ring with two maximal ideals. We also find bounds for the metric dimension of the annihilating-ideal graph of an arbitrary finite commutative principal ring.

Keywords

finite ringmetric dimensionannihilating-ideal graph

MSC classification

Primary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
Secondary: 13F10: Principal ideal rings 16P60: Chain conditions on annihilators and summands
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 3 , June 2021 , pp. 362 - 368
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

The author acknowledges the financial support from the Slovenian Research Agency (research core funding no. P1-0222).

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