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PreprintCC BY-SA 4.0arXiv

The Diametral Metric Dimension of Generalized Corona Graph

  • Anis Nur Fitria
  • Liliek Susilowati
  • Yayuk Wahyuni
  • Nor Haniza Sarmin
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Abstract

This study investigates the diametral metric dimension of generalized corona graphs, where the main graph is connected graph and the branch graphs form a sequence of connected graphs. The concept of diametral metric dimension is an extension of the metric dimension concept, requiring the resolving set to contain all diametral vertices. To determine the diametral metric dimension of a generalized corona graph, one must first identify the distance of each vertex in the graph and the graph's diametral set. Subsequently, a resolving set containing the diametral set is determined. The results show that the diametral metric dimension of the generalized corona graph depends on the diameter of the main graph and the metric dimensions of the graphs in the sequence. These concepts provide theoretical insights into resolving structures in the planning infrastructure and motivate further studies on other graph families and graph operations.

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Cite

BibTeXRIS
BibTeX
@misc{fitria2026diametral,
  title = {{The Diametral Metric Dimension of Generalized Corona Graph}},
  author = {Anis Nur Fitria and Liliek Susilowati and Yayuk Wahyuni and Nor Haniza Sarmin},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.21507},
  eprint = {2609.21507},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21507},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - The Diametral Metric Dimension of Generalized Corona Graph
AU  - Anis Nur Fitria
AU  - Liliek Susilowati
AU  - Yayuk Wahyuni
AU  - Nor Haniza Sarmin
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.21507
UR  - https://arxiv.org/abs/2609.21507
AB  - This study investigates the diametral metric dimension of generalized corona graphs, where the main graph is connected graph and the branch graphs form a sequence of connected graphs. The concept of diametral metric dimension is an extension of the metric dimension concept, requiring the resolving set to contain all diametral vertices. To determine the diametral metric dimension of a generalized corona graph, one must first identify the distance of each vertex in the graph and the graph's diametral set. Subsequently, a resolving set containing the diametral set is determined. The results show that the diametral metric dimension of the generalized corona graph depends on the diameter of the main graph and the metric dimensions of the graphs in the sequence. These concepts provide theoretical insights into resolving structures in the planning infrastructure and motivate further studies on other graph families and graph operations.
ER  -