Subsets of vertices of the same size and the same maximum distance

Authors

Maria Axenovich, Karlsruhe Institute of TechnologyFollow
Dominik DuerrschnabelFollow

Abstract

For a simple connected graph G=(V,E) and a subset X of its vertices, let

d*(X) = max {dist}_G(x,y): x,y ∈ X}

and let h*(G) be the largest k such that there are disjoint vertex subsets A and B of G, each of size k such that d*(A) = d*(B). Let h*(n) = min {h*(G): |V(G)|=n}. We prove that h*(n) =⌊(n+1)/3 ⌋, for n ≥ 6. This solves the homometric set problem restricted to the largest distance exactly. In addition we compare h*(G) with a respective function h_diam(G), where d*(A) is replaced with diam(G[A]).

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Axenovich, Maria and Duerrschnabel, Dominik (2018) "Subsets of vertices of the same size and the same maximum distance," Theory and Applications of Graphs: Vol. 5: Iss. 2, Article 7.
DOI: 10.20429/tag.2018.050207
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol5/iss2/7