English

Distance-unbalancedness of graphs

Combinatorics 2020-11-04 v1

Abstract

In this paper we propose and study a new structural invariant for graphs, called distance-unbalanced\-ness, as a measure of how much a graph is (un)balanced in terms of distances. Explicit formulas are presented for several classes of well-known graphs. Distance-unbalancedness of trees is also studied. A few conjectures are stated and some open problems are proposed.

Keywords

Cite

@article{arxiv.2011.01635,
  title  = {Distance-unbalancedness of graphs},
  author = {Štefko Miklavič and Primož Šparl},
  journal= {arXiv preprint arXiv:2011.01635},
  year   = {2020}
}

Comments

14 pages, 3 figures

R2 v1 2026-06-23T19:52:56.061Z