Forbidden Four Cycle, Star Graphs and Isometric Embeddings

Q: What type of study is this?

This is a Quantitative Study study.

Oleksiy Dovgoshey; Olga Rovenska

doi:10.48550/arxiv.2510.01667

October 2, 2025Open Access

Forbidden Four Cycle, Star Graphs and Isometric Embeddings

View Full Paper

Ask AI

Bookmark

Share

Key Points

Ultrametric spaces can be embedded into star graphs under specific conditions, allowing for rich mathematical relationships.
The findings establish that arbitrary infinite cardinalities can be accommodated in these embeddings, expanding graph theory's applications.
We employed rigorous proofs to demonstrate the sufficiency and necessity of the outlined conditions concerning these geometrical structures.
This work highlights the interplay between graph theory and metric spaces, prompting further exploration into related mathematical concepts.

Implication

This research reveals necessary conditions for isometric embeddings in ultrametric spaces, suggesting connections to labeled star graphs.

Abstract

We prove the necessary and sufficient conditions under which ultrametric spaces of arbitrary infinite cardinality admit isometric embeddings into ultrametric spaces generated by labeled star graphs.

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Dovgoshey et al. (2025) studied this question.

synapsesocial.com/papers/68e25385d6d66a53c2474cb8 https://doi.org/10.48550/arxiv.2510.01667

View Full Paper

Ask AI

Bookmark

Share

Forbidden Four Cycle, Star Graphs and Isometric Embeddings

Key Points

Implication

Abstract

Discussion

Cite This Study

Forbidden Four Cycle, Star Graphs and Isometric Embeddings

Key Points

Implication

Abstract

Discussion

Cite This Study

Keep reading

Keep reading