A Survey on Multiset Dimension and Its Variations

Azzah Albejani; Yuqing Lin; Joe Ryan; Kiki A. Sugeng

A Survey on Multiset Dimension and Its Variations

Combinatorics 2026-07-09 v1

Authors: Azzah Albejani , Yuqing Lin , Joe Ryan , Kiki A. Sugeng

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.

Cite

@article{arxiv.2607.08128,
  title  = {A Survey on Multiset Dimension and Its Variations},
  author = {Azzah Albejani and Yuqing Lin and Joe Ryan and Kiki A. Sugeng},
  journal= {arXiv preprint arXiv:2607.08128},
  year   = {2026}
}