English

Realization of distance matrices by graphs of genus 1

Combinatorics 2020-12-15 v1

Abstract

Given a distance matrix DD, we study the behavior of its compaction vector and reduction matrix with respect to the problem of the realization of DD by a weighted graph. To this end, we first give a general result on realization by nn-cycles and successively we mainly focus on graphs of genus 1, presenting an algorithm which determines when a distance matrix is realizable by such a kind of graph, and then, shows how to construct it.

Keywords

Cite

@article{arxiv.2012.07698,
  title  = {Realization of distance matrices by graphs of genus 1},
  author = {Cristiano Bocci and Chiara Capresi},
  journal= {arXiv preprint arXiv:2012.07698},
  year   = {2020}
}

Comments

22 pages, 15 figures