A Survey on Multiset Dimension and Its Variations

Authors

  • Azzah Albejani School of Computer and Information Sciences, The University of Newcastle, Australia; Department of Mathematics, Faculty of Science, University of Hafr Al Batin, Saudi Arabia
  • Yuqing Lin School of Computer and Information Sciences, The University of Newcastle, Australia
  • Joe Ryan School of Computer and Information Sciences, The University of Newcastle, Australia
  • Kiki A Sugeng Departments of Mathematics, University of Indonesia, Depok - Indonesia

DOI:

https://doi.org/10.19139/soic-2310-5070-4062

Keywords:

Metric Dimension, Metric Dimension Variations, Multiset Dimension, Outer Multiset Dimension, Local Multiset Dimension, Local Outer Multiset Dimension, Edge Multiset Dimension

Abstract

The classical notion of metric dimension has led to a wide range of extensions, such as the local, strong, fractional, and k-metric dimensions. This naturally raises the question of whether analogous variants can be formulated and studied within the multiset framework. While some progress has been made, particularly on the local multiset dimension, outer multiset dimension, local outer multiset dimension, and edge multiset dimension, however, the area remains far from fully explored. In this paper, we survey the existing variants and consolidate the results currently available in the literature. Furthermore, we identify several directions for future work.

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Published

2026-09-25

How to Cite

Albejani, A., Lin, Y., Ryan, J., & Sugeng, K. A. (2026). A Survey on Multiset Dimension and Its Variations. Statistics, Optimization & Information Computing, 16(5), 4960–4988. https://doi.org/10.19139/soic-2310-5070-4062

Issue

Vol. 16 No. 5 (2026)

Section

Research Articles

Categories

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Copyright (c) 2026 Azzah Albejani, Yuqing Lin, Joe Ryan, Kiki A Sugeng

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