Towards the essence of \v{S}olt\'es' problem
Stijn Cambie
TL;DR
This paper investigates graphs where total distance decreases upon vertex removal, providing insights and doubts regarding olte9s' problem, which concerns graphs with unchanged total distance after vertex removal.
Contribution
It offers new results and intuition about olte9s' problem, exploring the behavior of total distances in graphs when vertices are removed.
Findings
Results suggest certain graph structures affect total distance decrease.
Provides doubts and conjectures related to olte9s' problem.
Offers new perspectives on vertex removal impact on graph distances.
Abstract
We explore the question asking for graphs for which the total distance decreases, possibly by a fixed constant , upon the removal of any of its vertices. We obtain results leading to intuition and doubts for the \v{S}olt\'es' problem () and its conjectures.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Complexity and Algorithms in Graphs