Towards the essence of \v{S}olt\'es' problem

Stijn Cambie

Towards the essence of \v{S}olt\'es' problem

Combinatorics 2024-06-06 v1

Authors: Stijn Cambie

Abstract

We explore the question asking for graphs $G$ for which the total distance decreases, possibly by a fixed constant $k$ , upon the removal of any of its vertices. We obtain results leading to intuition and doubts for the \v{S}olt\'es' problem ( $k=0$ ) and its conjectures.

Keywords

graph theory total distance vertex removal Šoltés problem constant decrease conjectures

Cite

@article{arxiv.2406.03451,
  title  = {Towards the essence of \v{S}olt\'es' problem},
  author = {Stijn Cambie},
  journal= {arXiv preprint arXiv:2406.03451},
  year   = {2024}
}

Comments

11 pages, 6 figures

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