Multiset Partition Dimension of Graphs

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

Multiset Partition Dimension of Graphs

Combinatorics 2026-07-08 v1

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

Abstract

In this paper, we introduce the multiset partition dimension of graphs. This parameter extends the classical partition dimension to the multiset setting by considering multiset distances from vertices to parts of a vertex partition. We establish some fundamental properties of this parameter and determine its exact values for several important classes of graphs.

Cite

@article{arxiv.2607.07407,
  title  = {Multiset Partition Dimension of Graphs},
  author = {Azzah Albejania and Yuqing Lin and Joe Ryan and Kiki A. Sugeng},
  journal= {arXiv preprint arXiv:2607.07407},
  year   = {2026}
}